[
 {
  "id": "thomson1874-date",
  "author": "William Thomson",
  "work": "William Thomson (later Lord Kelvin), \"The Kinetic Theory of the Dissipation of Energy\" (item 9 of the meeting of 16 February 1874)",
  "year": 1874,
  "venue": "Proceedings of the Royal Society of Edinburgh, vol. 8 (Session 1873-74; volume dated 1872-1875), pp. 325-334. DOI 10.1017/S0370164600029680. Reprinted in Nature 9 (9 April 1874) 441-444, DOI 10.1038/009441c0",
  "page": "p. 289 (meeting heading) and p. 325 (paper heading)",
  "url_fetched": "https://archive.org/download/proceedingso818721875roya/proceedingso818721875roya_djvu.txt",
  "file_saved": "research/arrow-of-time/sources/archiveorg_ProcRSE_v8_1872-75_proceedingso818721875roya_djvu.txt",
  "lang": "en",
  "verbatim": "Monday, 16th February 1874. Sir W. THOMSON, President, in the Chair. [...] The following Communications were read :— 9. The Kinetic Theory of the Dissipation of Energy. By Sir William Thomson.",
  "translation_note": "n/a (English)",
  "confidence_note": "Archive.org OCR (djvu.txt). The meeting heading on p. 289 is followed by eight obituary notices (items 1-8) and the Fellows statement, with no intervening meeting heading until \"Monday, 2d March 1874\" (p. 335ff.), so the paper was read on Monday 16 February 1874. Ellipsis [...] marks omitted material (obituaries etc., pp. 289-325). Note: the volume printed his name as \"Sir William Thomson\"; he became Lord Kelvin in 1892."
 },
 {
  "id": "thomson1874-abstract-dynamics",
  "author": "William Thomson",
  "work": "William Thomson (later Lord Kelvin), \"The Kinetic Theory of the Dissipation of Energy\" (item 9 of the meeting of 16 February 1874)",
  "year": 1874,
  "venue": "Proceedings of the Royal Society of Edinburgh, vol. 8 (Session 1873-74; volume dated 1872-1875), pp. 325-334. DOI 10.1017/S0370164600029680. Reprinted in Nature 9 (9 April 1874) 441-444, DOI 10.1038/009441c0",
  "page": "p. 325",
  "url_fetched": "https://archive.org/download/proceedingso818721875roya/proceedingso818721875roya_djvu.txt",
  "file_saved": "research/arrow-of-time/sources/archiveorg_ProcRSE_v8_1872-75_proceedingso818721875roya_djvu.txt",
  "lang": "en",
  "verbatim": "In abstract dynamics the instantaneous reversal of the motion of every moving particle of a system causes the system to move backwards, each particle of it along its old path, and at the same speed as before, when again in the same position. That is to say, in mathematical language, any solution remains a solution when t is changed into -t. In physical dynamics this simple and perfect reversibility fails, on account of forces depending on friction of solids; imperfect fluidity of fluids; imperfect elasticity of solids; inequalities of temperature, and consequent conduction of heat produced by stresses in solids and fluids; imperfect magnetic retentiveness; residual electric polarisation of dielectrics; generation of heat by electric currents induced by motion; diffusion of fluids, solution of solids in fluids, and other chemical changes; and absorption of radiant heat and light.",
  "ocr_raw": "... any solution remains a solution when t is changed into - 1. In physical dynamics ... friction of solids ; imperfect fluidity of fluids ; ...",
  "translation_note": "n/a (English)",
  "confidence_note": "Archive.org OCR, lightly corrected: OCR \"- 1\" corrected to \"-t\" (the Nature reprint OCR reads \"changed into [em dash]t\", and the sense requires t -> -t); spaces before semicolons normalised; line-end hyphens joined. The Nature reprint (9 April 1874) has the same sentence with \"an instantaneous reversal\"."
 },
 {
  "id": "thomson1874-reversed-world",
  "author": "William Thomson",
  "work": "William Thomson (later Lord Kelvin), \"The Kinetic Theory of the Dissipation of Energy\" (item 9 of the meeting of 16 February 1874)",
  "year": 1874,
  "venue": "Proceedings of the Royal Society of Edinburgh, vol. 8 (Session 1873-74; volume dated 1872-1875), pp. 325-334. DOI 10.1017/S0370164600029680. Reprinted in Nature 9 (9 April 1874) 441-444, DOI 10.1038/009441c0",
  "page": "pp. 325-326",
  "url_fetched": "https://archive.org/download/proceedingso818721875roya/proceedingso818721875roya_djvu.txt",
  "file_saved": "research/arrow-of-time/sources/archiveorg_ProcRSE_v8_1872-75_proceedingso818721875roya_djvu.txt",
  "lang": "en",
  "verbatim": "The essence of Joule’s discovery is the subjection of physical phenomena to dynamical law. If, then, the motion of every particle of matter in the universe were precisely reversed at any instant, the course of nature would be simply reversed for ever after. The bursting bubble of foam at the foot of a waterfall would reunite and descend into the water; the thermal motions would reconcentrate their energy, and throw the mass up the fall in drops re-forming into a close column of ascending water. Heat which had been generated by the friction of solids and dissipated by conduction, and radiation with absorption, would come again to the place of contact, and throw the moving body back against the force to which it had previously yielded. Boulders would recover from the mud the materials required to rebuild them into their previous jagged forms, and would become reunited to the mountain peak from which they had formerly broken away. And if also the materialistic hypothesis of life were true, living creatures would grow backwards, with conscious knowledge of the future, but no memory of the past, and would become again unborn. But the real phenomena of life infinitely transcend human science, and speculation regarding consequences of their imagined reversal is utterly unprofitable. Far otherwise, however, is it in respect to the reversal of the motions of matter uninfluenced by life, a very elementary consideration of which leads to the full explanation of the theory of dissipation of energy.",
  "ocr_raw": "If, then, the motion of every par- 326 Proceedings of the Poyal Society tide of matter in tlie universe were precisely reversed at any instant, ... the water ; the thermal motions ...",
  "translation_note": "n/a (English)",
  "confidence_note": "Archive.org OCR, corrected: \"par- [page break] tide\" -> \"particle\" (Nature reprint OCR reads \"every particle of matter\"), \"tlie\" -> \"the\", running head \"326 Proceedings of the Poyal Society\" removed; page break falls inside \"par-ticle\" (p. 325/326)."
 },
 {
  "id": "thomson1874-reversal-of-gas",
  "author": "William Thomson",
  "work": "William Thomson (later Lord Kelvin), \"The Kinetic Theory of the Dissipation of Energy\" (item 9 of the meeting of 16 February 1874)",
  "year": 1874,
  "venue": "Proceedings of the Royal Society of Edinburgh, vol. 8 (Session 1873-74; volume dated 1872-1875), pp. 325-334. DOI 10.1017/S0370164600029680. Reprinted in Nature 9 (9 April 1874) 441-444, DOI 10.1038/009441c0",
  "page": "p. 329",
  "url_fetched": "https://archive.org/download/proceedingso818721875roya/proceedingso818721875roya_djvu.txt",
  "file_saved": "research/arrow-of-time/sources/archiveorg_ProcRSE_v8_1872-75_proceedingso818721875roya_djvu.txt",
  "lang": "en",
  "verbatim": "Suppose now the temperature to have become thus very approximately equalised at a certain time from the beginning, and let the motion of every particle become instantaneously reversed. Each molecule will retrace its former path, and at the end of a second interval of time, equal to the former, every molecule will be in the same position, and moving with the same velocity, as at the beginning; so that the given initial unequal distribution of temperature will again be found, with only the difference that each particle is moving in the direction reverse to that of its initial motion. This difference will not prevent an instantaneous subsequent commencement of equalisation, which, with entirely different paths for the individual molecules, will go on in the average according to the same law as that which took place immediately after the system was first left to itself.",
  "translation_note": "n/a (English)",
  "confidence_note": "Archive.org OCR; no substantive corrections needed (only spacing and a space before \";\" normalised). Page image of p. 329 downloaded but not separately proof-read."
 },
 {
  "id": "thomson1874-imprecise-reversal",
  "author": "William Thomson",
  "work": "William Thomson (later Lord Kelvin), \"The Kinetic Theory of the Dissipation of Energy\" (item 9 of the meeting of 16 February 1874)",
  "year": 1874,
  "venue": "Proceedings of the Royal Society of Edinburgh, vol. 8 (Session 1873-74; volume dated 1872-1875), pp. 325-334. DOI 10.1017/S0370164600029680. Reprinted in Nature 9 (9 April 1874) 441-444, DOI 10.1038/009441c0",
  "page": "pp. 329-330",
  "url_fetched": "https://archive.org/download/proceedingso818721875roya/proceedingso818721875roya_djvu.txt",
  "file_saved": "research/arrow-of-time/sources/archiveorg_ProcRSE_v8_1872-75_proceedingso818721875roya_djvu.txt ; page image research/arrow-of-time/sources/page_images/ProcRSE8_leaf356.jpg (p. 330)",
  "lang": "en",
  "verbatim": "By merely looking on crowds of molecules, and reckoning their energy in the gross, we could not discover that in the very special case we have just considered the progress was towards a succession of states, in which the distribution of energy deviates more and more from uniformity up to a certain time. The number of molecules being finite, it is clear that small finite deviations from absolute precision in the reversal we have supposed would not obviate the resulting disequalisation of the distribution of energy. But the greater the number of molecules, the shorter will be the time during which the disequalising will continue; and it is only when we regard the number of molecules as practically infinite that we can regard spontaneous disequalisation as practically impossible.",
  "translation_note": "n/a (English)",
  "confidence_note": "OCR (p. 329 part) + visually checked against page image of p. 330. IMPORTANT for the page: Thomson does NOT say that a slight error makes the reversed motion fail; he says small finite deviations would NOT obviate the disequalisation, but that the larger the number of molecules the shorter the time during which the (anti-thermodynamic) disequalising continues. No \"instability\"/\"chaos\" language appears."
 },
 {
  "id": "thomson1874-recurrence-and-bar",
  "author": "William Thomson",
  "work": "William Thomson (later Lord Kelvin), \"The Kinetic Theory of the Dissipation of Energy\" (item 9 of the meeting of 16 February 1874)",
  "year": 1874,
  "venue": "Proceedings of the Royal Society of Edinburgh, vol. 8 (Session 1873-74; volume dated 1872-1875), pp. 325-334. DOI 10.1017/S0370164600029680. Reprinted in Nature 9 (9 April 1874) 441-444, DOI 10.1038/009441c0",
  "page": "p. 330",
  "url_fetched": "https://archive.org/download/proceedingso818721875roya/proceedingso818721875roya_djvu.txt",
  "file_saved": "research/arrow-of-time/sources/archiveorg_ProcRSE_v8_1872-75_proceedingso818721875roya_djvu.txt ; page image research/arrow-of-time/sources/page_images/ProcRSE8_leaf356.jpg",
  "lang": "en",
  "verbatim": "And, in point of fact, if any finite number of perfectly elastic molecules, however great, be given in motion in the interior of a perfectly rigid vessel, and be left for a sufficiently long time undisturbed except by mutual impact and collisions against the sides of the containing vessel, it must happen over and over again that (for example) something more than 9/10ths of the whole energy shall be in one-half of the vessel, and less than 1/10th of the whole energy in the other half. But if the number of molecules be very great, this will happen enormously less frequently than that something more than 6/10ths shall be in one-half, and something less than 4/10ths in the other. [...] It is a strange but nevertheless a true conception of the old well-known law of the conduction of heat, to say that it is very improbable that in the course of 1000 years one-half of the bar of iron shall of itself become warmer by a degree than the other half; and that the probability of this happening before 1,000,000 years pass is 1000 times as great as that it will happen in the course of 1000 years, and that it certainly will happen in the course of some very long time. But let it be remembered that we have supposed the bar to be covered with an impermeable varnish. Do away with this impossible ideal, and believe the number of molecules in the universe to be infinite; then we may say one-half of the bar will never become warmer than the other, except by the agency of external sources of heat or cold.",
  "ocr_raw": "... something more than x9xths of the whole energy shall be in one-half of the vessel, and less than xVth of the whole energy in the other half. ... something more than x6oths shall be in one-half, and something less than x4xths in the other. ...",
  "translation_note": "n/a (English)",
  "confidence_note": "Fractions were garbled in OCR; corrected by reading the page image (printed as stacked fractions 9/10, 1/10, 6/10, 4/10). Ellipsis [...] omits one sentence about the unit of time. Visually verified against page image."
 },
 {
  "id": "thomson1874-probability-numbers",
  "author": "William Thomson",
  "work": "William Thomson (later Lord Kelvin), \"The Kinetic Theory of the Dissipation of Energy\" (item 9 of the meeting of 16 February 1874)",
  "year": 1874,
  "venue": "Proceedings of the Royal Society of Edinburgh, vol. 8 (Session 1873-74; volume dated 1872-1875), pp. 325-334. DOI 10.1017/S0370164600029680. Reprinted in Nature 9 (9 April 1874) 441-444, DOI 10.1038/009441c0",
  "page": "pp. 330-331 (text); Appendix pp. 331-334",
  "url_fetched": "https://archive.org/download/proceedingso818721875roya/proceedingso818721875roya_djvu.txt",
  "file_saved": "research/arrow-of-time/sources/archiveorg_ProcRSE_v8_1872-75_proceedingso818721875roya_djvu.txt ; page image research/arrow-of-time/sources/page_images/ProcRSE8_leaf357.jpg (p. 331)",
  "lang": "en",
  "verbatim": "Take however another case, in which the probability may be readily calculated. Let a hermetically sealed glass jar of air contain 2,000,000,000,000 molecules of oxygen, and 8,000,000,000,000 molecules of nitrogen. If examined any time in the infinitely distant future, what is the number of chances against one that all the molecules of oxygen and none of nitrogen shall be found in one stated part of the vessel equal in volume to 1/5th of the whole? The number expressing the answer in the Arabic notation has about 2,173,220,000,000 of places of whole numbers. On the other hand, the chance against their being exactly 2/10ths of the whole number of particles of nitrogen, and at the same time exactly 2/10ths of the whole number of particles of oxygen in the first specified part of the vessel, is only 4021 × 10^9 to 1.",
  "ocr_raw": "... equal in volume to |th of the whole? The number expressing the answer in the Arabic notation has about 2,173,220,000,000 of places of whole numbers. On the other hand, the chance against their being exactly -^ths of the whole number of particles of nitrogen, and at the same time exactly T%ths of the whole number of particles of oxygen in the first specified part of the vessel, is only 4021 x 109 to 1.",
  "translation_note": "n/a (English)",
  "confidence_note": "Numbers verified against the page image of p. 331 (the digit groups of 2,173,220,000,000 were counted on a zoomed crop: 2|173|220|000|000, i.e. about 2.17322 x 10^12 digits). \"1/5th\", \"2/10ths\", and \"10^9\" are printed as a stacked fraction / superscript. The Appendix (p. 333) gives: \"log N = 10^13 - 26 x 10^12 x log 2 = (10 - 26 log 2) x 10^12 = 2173220 x 10^6\" [verified against the page image of p. 333, which also states the hypothesis a/(a+b) = 2/10, b/(a+b) = 8/10 and the required probability 2^(26 x 10^12) / 10^(10^13)], and p. 334 gives the second figure as 1/(2 pi ef sqrt(n n')) = 1/(4021 x 10^9). The Nature reprint OCR also reads \"about 2,173,220,000,000 of places\" and \"4021 X Io’ to l\"."
 },
 {
  "id": "thomson1874-nature-reprint",
  "author": "William Thomson",
  "work": "\"Kinetic Theory of the Dissipation of Energy\" (unsigned heading in Nature; byline at end)",
  "year": 1874,
  "venue": "Nature 9, no. 232 (9 April 1874) 441-444. DOI 10.1038/009441c0 (Crossref)",
  "page": "p. 441",
  "url_fetched": "https://archive.org/download/sim_nature-uk_1874-04-09_9_232/sim_nature-uk_1874-04-09_9_232_djvu.txt",
  "file_saved": "research/arrow-of-time/sources/archiveorg_Nature_1874-04-09_v9_iss232_djvu.txt",
  "lang": "en",
  "verbatim": "In abstract dynamics an instantaneous reversal of the motion of every moving particle of a system causes the system to move backwards, each particle of it along its old path, and at the same speed as before when again in the same position",
  "ocr_raw": "[* abstract dynamics an instantaneous reversal of the motion of every moving particle of a system causes the system to move backwards, each particle of it along its old path, and at the same speed as before when again in the same position",
  "translation_note": "n/a (English)",
  "confidence_note": "Archive.org OCR of the Nature issue; drop-cap \"In\" mis-read as \"[*\". Confirms the reprint text is essentially identical to Proc. RSE (small differences: \"an\" vs \"the\" instantaneous reversal; punctuation)."
 },
 {
  "id": "loschmidt1876-reversal",
  "author": "Josef Loschmidt",
  "work": "Josef Loschmidt, \"Über den Zustand des Wärmegleichgewichtes eines Systems von Körpern mit Rücksicht auf die Schwerkraft. I.\"",
  "year": 1876,
  "venue": "Sitzungsberichte der kaiserlichen Akademie der Wissenschaften, math.-naturw. Classe, Bd. 73, II. Abtheilung (Jahrgang 1876), pp. 128-142. Presented at the session of 27 January 1876 (per the session report printed in Abt. III of vol. 73).",
  "page": "p. 139",
  "url_fetched": "https://viewer.acdh.oeaw.ac.at/viewer/image/MN_2Abt_73_1876/156/ (IIIF image of canvas 156 = printed p. 139, fetched via https://viewer.acdh.oeaw.ac.at/viewer/api/v1/records/MN_2Abt_73_1876/manifest/)",
  "file_saved": "research/arrow-of-time/sources/page_images/MN_2Abt_73_1876_canvas156.jpg ; OCR: research/arrow-of-time/sources/ocr_tesseract/MN_2Abt_73_1876_canvas156.txt ; research/arrow-of-time/sources/OAW_WienerBer_73_II_1876_Loschmidt_I_pp128-142_tesseract.txt",
  "lang": "de",
  "verbatim": "Übrigens muss man mit der Behauptung, dass in einem Systeme, in welchem sich der sogenannte stationäre Zustand aus einem anderen beliebigen Anfangszustande hergestellt hat, dieser Durchschnittszustand sich nun für alle Zeiten selbst aufrecht erhalten werde, vorsichtig sein. Ich glaube vielmehr, dass man diese Voraussage nur für eine kurze Zeit mit voller Zuversicht machen dürfe.\n\nDenn wenn wir im obigen Falle, nachdem eine zur Herstellung des stationären Zustandes vollkommen ausreichende Zeit τ verstrichen ist, plötzlich die Geschwindigkeiten aller Atome in entgegengesetzter Richtung annehmen, so würden wir damit am Beginne eines Zustandes stehen, dem ebenfalls der Charakter des Stationären zuzukommen scheinen würde. Für geraume Zeit wäre das wohl richtig, aber allmälig würde sich der stationäre Zustand gleichsam deterioriren, und nach dem Verlaufe der Zeit τ wären wir unfehlbar wieder bei unserem Anfangszustande angekommen: ein einziges Atom m₁ hätte die gesammte lebendige Kraft des Systemes absorbirt, und durch seine Erhebung zur oberen Gefässwand in Spannkraft umgesetzt, während alle anderen regungslos auf ihren alten Plätzen am Boden liegen.\n\nOffenbar muss ganz allgemein, in jedem beliebigen System, der gesammte Verlauf der Begebenheiten rückläufig werden, wenn momentan die Geschwindigkeiten aller seiner Elemente umgekehrt werden.\n\nDas berühmte Problem, Geschehenes ungeschehen zu machen, hat damit zwar keine Lösung, doch eine einfache Formulirung erhalten, welche in der simplen Anweisung besteht, die momentanen Geschwindigkeiten aller Atome des Universums plötzlich umzukehren.",
  "ocr_raw": "... dass in einem Systeme, in welchem sich der sogenannte stationäre Zustand aus einem anderen beliebigen Anfangszustande hergestellt hat, die- ser Durehschnittszustand ... Zeit x verstrichen ist ... der Zeit x wären wir ... ein einziges Atom m, hätte ... der gesammte Verlauf der Begebenheiten riekläufig werden, wenn momentan die Gesehwindigkeiten aller seiner Elemente \"u umgekehrt werden. ... Formu- lirvung erhalten ... des Universums 1) plötzlich umzukehren, | il",
  "translation_note": "Our translation: \"Incidentally, one must be cautious with the claim that in a system in which the so-called stationary state has arisen from some other arbitrary initial state, this average state will now maintain itself for all time. I believe rather that one may make this prediction with full confidence only for a short time. For if, in the above case, after a time τ fully sufficient for the establishment of the stationary state has elapsed, we suddenly give all the atoms velocities in the opposite direction, we would thereby stand at the beginning of a state which would likewise appear to have the character of the stationary. For a considerable time that would indeed be correct, but gradually the stationary state would, as it were, deteriorate, and after the lapse of the time τ we would infallibly have arrived back at our initial state: a single atom m₁ would have absorbed the entire vis viva of the system and, by rising to the upper wall of the vessel, converted it into potential energy [Spannkraft], while all the others lie motionless at their old places on the floor. Evidently, quite generally, in any system whatever, the entire course of events must become retrograde if at some moment the velocities of all its elements are reversed. The famous problem of making what has happened un-happen has thereby received, not a solution, but a simple formulation, which consists in the simple instruction: suddenly reverse the momentary velocities of all atoms of the universe.\" (ours)",
  "confidence_note": "Transcribed by us from the page image (ÖAW digitisation, 1800px) and cross-checked with our own Tesseract (deu) OCR; OCR errors listed in ocr_raw were corrected by reading the image. The example is Loschmidt's gravity model (all atoms initially at rest on the floor except one atom m₁ dropped from the top). NOTE: in Part I Loschmidt does not phrase this explicitly as an objection to Boltzmann's H-theorem; the general statement \"Offenbar muss ganz allgemein...\" is the reversal argument. Boltzmann (1877, Bd. 75, p. 67) reads it as \"ein Bedenken gegen die Möglichkeit eines rein mechanischen Beweises des zweiten Hauptsatzes\". Part II of Loschmidt (vol. 73, pp. 366-372) and Parts III-IV (vol. 75, 76) were NOT examined."
 },
 {
  "id": "loschmidt1876-conclusion-p140",
  "author": "Josef Loschmidt",
  "work": "Josef Loschmidt, \"Über den Zustand des Wärmegleichgewichtes eines Systems von Körpern mit Rücksicht auf die Schwerkraft. I.\"",
  "year": 1876,
  "venue": "Sitzungsberichte der kaiserlichen Akademie der Wissenschaften, math.-naturw. Classe, Bd. 73, II. Abtheilung (Jahrgang 1876), pp. 128-142. Presented at the session of 27 January 1876 (per the session report printed in Abt. III of vol. 73).",
  "page": "p. 140",
  "url_fetched": "https://viewer.acdh.oeaw.ac.at/viewer/image/MN_2Abt_73_1876/157/",
  "file_saved": "research/arrow-of-time/sources/page_images/MN_2Abt_73_1876_canvas157.jpg ; research/arrow-of-time/sources/OAW_WienerBer_73_II_1876_Loschmidt_I_pp128-142_tesseract.txt",
  "lang": "de",
  "verbatim": "Nachdem wir im Vorhergehenden gezeigt haben, dass für die Constanz der Temperatur eines Körpers in allen seinen Theilen im Zustande des Wärmegleichgewichtes bisher ein strikter Beweis nicht geliefert ist, und dass der vermeintliche Widerspruch des zweiten Hauptsatzes mit der gegentheiligen Annahme nicht existirt, und nachdem wir für einige specielle Fälle das Nichtzutreffen jenes Ausspruches direct nachgewiesen haben, tritt an uns die Aufgabe heran, selber die Aufstellung eines allgemeinen Gesetzes der Abhängigkeit der Temperatur von der verticalen Ausdehnung zu versuchen",
  "translation_note": "Our translation: \"Having shown in the foregoing that no strict proof has so far been given for the constancy of a body's temperature in all its parts in the state of thermal equilibrium, and that the supposed contradiction between the second law and the contrary assumption does not exist, and having directly demonstrated for some special cases that that statement does not hold, we are faced with the task of ourselves attempting to set up a general law of the dependence of temperature on vertical extent\" (ours).",
  "confidence_note": "Visually verified against page image (section heading \"Allgemeines Gesetz der Abhängigkeit der Temperaturen von der Höhe.\"). Shows Loschmidt's actual target: the claim that equilibrium temperature is uniform under gravity."
 },
 {
  "id": "loschmidt1876-thomson-citation",
  "author": "Josef Loschmidt",
  "work": "Josef Loschmidt, \"Über den Zustand des Wärmegleichgewichtes eines Systems von Körpern mit Rücksicht auf die Schwerkraft. I.\"",
  "year": 1876,
  "venue": "Sitzungsberichte der kaiserlichen Akademie der Wissenschaften, math.-naturw. Classe, Bd. 73, II. Abtheilung (Jahrgang 1876), pp. 128-142. Presented at the session of 27 January 1876 (per the session report printed in Abt. III of vol. 73).",
  "page": "p. 135 (context p. 134)",
  "url_fetched": "https://viewer.acdh.oeaw.ac.at/viewer/image/MN_2Abt_73_1876/152/",
  "file_saved": "research/arrow-of-time/sources/ocr_tesseract/MN_2Abt_73_1876_canvas152.txt ; research/arrow-of-time/sources/OAW_WienerBer_73_II_1876_Loschmidt_I_pp128-142_tesseract.txt",
  "lang": "de/en",
  "verbatim": "Aus diesen Betrachtungen ergibt sich die merkwürdige Folgerung, dass man zwar aus dem Axiom von Clausius: „Es ist unmöglich, Wärme von einem kälteren zu einem wärmeren Körper ohne Compensation zu überführen“, oder aus dem äquivalenten von W. Thomson: „It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects“. (Transactions of the Royal Society of Edinburgh 17. March 1851. Vol. XX, p. 265) den zweiten Hauptsatz ableiten kann, dass aber die Umkehrung dieses Verfahrens nicht erlaubt ist, weil der Umfang des zweiten Satzes ein weiterer ist als derjenige jener Axiome.",
  "ocr_raw": "... „It. is impossible, by means of | inanimate material ageney, ... coldest of the surrounding objeets“. (Transactions of the Royal I | Society of Edinburgh 17..March 1851. Vol. XX, p. 265) den I zweiten Hauptsatz ...",
  "translation_note": "Our translation: \"From these considerations follows the remarkable conclusion that one can indeed derive the second law from Clausius's axiom ... or from the equivalent one of W. Thomson ..., but that the reverse of this procedure is not permitted, because the scope of the second law is wider than that of those axioms.\" (ours)",
  "confidence_note": "Tesseract OCR, corrected for obvious OCR noise only (not visually proof-read line by line). ANSWER TO \"does he cite Thomson?\": In Part I the only Thomson references found (OCR search, pp. 128-142) are this 1851 second-law axiom (and a mention on p. 134 of \"W. Thomson und R. Clausius\" treating that axiom as basic). No reference to Thomson's 1874 \"Kinetic Theory of the Dissipation of Energy\" was found in Part I."
 },
 {
  "id": "loschmidt1876-presented",
  "author": "(Academy session report)",
  "work": "Session report \"III. Sitzung vom 27. Jänner 1876\"",
  "year": 1876,
  "venue": "Sitzungsberichte ... math.-naturw. Classe Bd. 73, III. Abtheilung (Google scan on archive.org, item sitzungsbericht188klasgoog)",
  "page": "session report, p. 32 (printed page number as OCR'd; not verified)",
  "url_fetched": "https://archive.org/download/sitzungsbericht188klasgoog/sitzungsbericht188klasgoog_djvu.txt",
  "file_saved": "research/arrow-of-time/sources/archiveorg_WienerBer_v73_1876_AbtIII_sessionreports_sitzungsbericht188klasgoog_djvu.txt",
  "lang": "de",
  "verbatim": "III. SITZUNG VOM 27. JÄNNER 1876. [...] Das w. M. Herr Prof. Loschmidt überreicht eine Abhandlung: „Über den Zustand des Wärmegleichgewichtes eines Systems von Körpern mit Rücksicht auf die Schwerkraft.“",
  "ocr_raw": "IIL SITZUNG VOM 27. JÄNNER 1876. ... Das w. M. Herr Prof. Loschmidt überreicht eine Abband- lung: „Über den Zustand des Wärmegleichgewicbtes eines Systems von Körpern mit Rücksicht ^uf die Schwerkraft.\"",
  "translation_note": "Our translation: \"Session III of 27 January 1876. [...] The full member Prof. Loschmidt presents a paper: ...\" (ours)",
  "confidence_note": "Archive.org OCR of a Google scan; obvious OCR errors corrected. Same volume reports Part II presented at \"VII. Sitzung vom 9. März 1876\". Vol. 75 Abt. III (sitzungsbericht292klasgoog) reports Part III presented 8 Feb 1877 and Boltzmann's \"Bemerkungen\" submitted at the session of 11 Jan 1877 (OCR)."
 },
 {
  "id": "boltzmann1877a-opening-II",
  "author": "Ludwig Boltzmann",
  "work": "Ludwig Boltzmann, \"Bemerkungen über einige Probleme der mechanischen Wärmetheorie\", Section II: \"Über die Beziehung eines allgemeinen mechanischen Satzes zum zweiten Hauptsatze der Wärmetheorie\"",
  "year": 1877,
  "venue": "Sitzungsberichte der kaiserlichen Akademie der Wissenschaften, math.-naturw. Classe, Bd. 75, II. Abtheilung (Jahrgang 1877), pp. 62-100 (Section II = pp. 67-73). Submitted at the session of 11 January 1877.",
  "page": "p. 67",
  "url_fetched": "https://viewer.acdh.oeaw.ac.at/viewer/image/MN_2Abt_75_1877/71/",
  "file_saved": "research/arrow-of-time/sources/page_images/MN_2Abt_75_1877_canvas071.jpg ; research/arrow-of-time/sources/OAW_WienerBer_75_II_1877_Boltzmann_Bemerkungen_pp62-100_tesseract.txt",
  "lang": "de",
  "verbatim": "In seiner Abhandlung über den Zustand des Wärmegleichgewichtes eines Systems von Körpern, mit Rücksicht auf die Schwerkraft, hat Loschmidt einen Satz ausgesprochen, welcher ein Bedenken gegen die Möglichkeit eines rein mechanischen Beweises des zweiten Hauptsatzes involvirt. Da dasselbe äusserst scharfsinnig erdacht ist und mir für das richtige Verständniss des zweiten Hauptsatzes von hoher Bedeutung zu sein scheint, an der bezeichneten Stelle aber eine mehr philosophische Einkleidung gefunden hat, in der es vielleicht manchem Physiker nur schwer verständlich sein wird, so will ich zunächst versuchen, es mit anderen Worten wiederzugeben.",
  "ocr_raw": "... hat Losehmidt einen Satz ausgesprochen, welcher ein Bedenken gegen die Möglichkeit eines rein mechanischen Beweises des zweiten Hauptsatzes involvirt: Da dasselbe ...",
  "translation_note": "Our translation: \"In his paper on the state of thermal equilibrium of a system of bodies with regard to gravity, Loschmidt has stated a theorem which casts doubt on the possibility of a purely mechanical proof of the second law. Since it is extremely ingeniously conceived and seems to me of great importance for the correct understanding of the second law, but has found at that place a rather philosophical dress in which it will perhaps be hard for some physicists to understand, I will first try to restate it in other words.\" (ours)",
  "confidence_note": "Visually verified against the page image. (\"Loschmidt\" is letter-spaced in the original.)"
 },
 {
  "id": "boltzmann1877a-restatement",
  "author": "Ludwig Boltzmann",
  "work": "Ludwig Boltzmann, \"Bemerkungen über einige Probleme der mechanischen Wärmetheorie\", Section II: \"Über die Beziehung eines allgemeinen mechanischen Satzes zum zweiten Hauptsatze der Wärmetheorie\"",
  "year": 1877,
  "venue": "Sitzungsberichte der kaiserlichen Akademie der Wissenschaften, math.-naturw. Classe, Bd. 75, II. Abtheilung (Jahrgang 1877), pp. 62-100 (Section II = pp. 67-73). Submitted at the session of 11 January 1877.",
  "page": "pp. 68-69",
  "url_fetched": "https://viewer.acdh.oeaw.ac.at/viewer/image/MN_2Abt_75_1877/72/ and https://viewer.acdh.oeaw.ac.at/viewer/image/MN_2Abt_75_1877/73/",
  "file_saved": "research/arrow-of-time/sources/page_images/MN_2Abt_75_1877_canvas073.jpg ; research/arrow-of-time/sources/OAW_WienerBer_75_II_1877_Boltzmann_Bemerkungen_pp62-100_tesseract.txt",
  "lang": "de",
  "verbatim": "[...] Sämmtliche materiellen Punkte sollen zu Anfang der Zeit, also zur Zeit Null dieselben Positionen haben, welche sie im Verlaufe der den früheren Anfangsbedingungen entsprechenden Bewegung zur Zeit t₁ hatten und auch ganz dieselben aber entgegengesetzt gerichteten Geschwindigkeiten. [...] Es ist klar, dass die materiellen Punkte dieselben Zustände, die sie unter den früheren Anfangsbedingungen in directer Weise durchliefen, jetzt in der verkehrten Weise durchlaufen werden. [...] Über das Vorzeichen dieses Integrales kann also nicht aus dem Wirkungsgesetze der Kräfte, sondern blos aus den Anfangsbedingungen ein Schluss gezogen werden. Dass dieses Integrale bei allen Vorgängen der Welt, in welcher wir leben, wie die Erfahrung lehrt [Ungleichheitszeichen, s. Anm.] 0 ist, ist nicht in dem Wirkungsgesetze der in derselben vorhandenen Kräfte, sondern bloss in den Anfangsbedingungen begründet.",
  "ocr_raw": "... Sämmtliche materiellen Punkte! sollen zu An- [p. 68/69] fang der Zeit ... zur Zeit {, hatten ... gelehrt = 0 ist ...",
  "translation_note": "Our translation: \"[...] All material points are to have at the beginning of time, i.e. at time zero, the same positions that they had at time t₁ in the course of the motion corresponding to the earlier initial conditions, and also exactly the same but oppositely directed velocities. [...] It is clear that the material points will now traverse in the reverse order the same states which under the earlier initial conditions they traversed in the direct order. [...] Thus no conclusion about the sign of this integral [∫dQ/T] can be drawn from the law of action of the forces, but only from the initial conditions. That this integral, in all processes of the world in which we live, is [sign] 0, as experience teaches, is grounded not in the law of action of the forces present in it, but solely in the initial conditions.\" (ours)",
  "confidence_note": "p. 69 visually verified against page image. The integral referred to is ∫dQ/T; the relation signs printed on p. 69 (in the displayed formulas and in the quoted sentence \"lehrt ... 0 ist\") are composite inequality glyphs (stacked less/greater/equal strokes) that we could not identify with certainty from the scan, so we replaced the one in the quoted sentence by a bracketed placeholder rather than guess. On pp. 67 and 70 the sign is clearly ≦ (less than or equal). The p. 68 fragment (first sentence) is from OCR and ends a sentence that starts on p. 68 (\"Wir wollen jetzt an die Stelle der früheren Anfangsbedingungen folgende setzen: Sämmtliche materiellen Punkte sollen zu An-\")."
 },
 {
  "id": "boltzmann1877a-sophisma",
  "author": "Ludwig Boltzmann",
  "work": "Ludwig Boltzmann, \"Bemerkungen über einige Probleme der mechanischen Wärmetheorie\", Section II: \"Über die Beziehung eines allgemeinen mechanischen Satzes zum zweiten Hauptsatze der Wärmetheorie\"",
  "year": 1877,
  "venue": "Sitzungsberichte der kaiserlichen Akademie der Wissenschaften, math.-naturw. Classe, Bd. 75, II. Abtheilung (Jahrgang 1877), pp. 62-100 (Section II = pp. 67-73). Submitted at the session of 11 January 1877.",
  "page": "p. 70",
  "url_fetched": "https://viewer.acdh.oeaw.ac.at/viewer/image/MN_2Abt_75_1877/74/",
  "file_saved": "research/arrow-of-time/sources/page_images/MN_2Abt_75_1877_canvas074.jpg ; research/arrow-of-time/sources/OAW_WienerBer_75_II_1877_Boltzmann_Bemerkungen_pp62-100_tesseract.txt",
  "lang": "de",
  "verbatim": "Jeder Versuch aus der Natur der Körper und dem Wirkungsgesetze der zwischen ihnen thätigen Kräfte, ohne Hinzuziehung der Anfangsbedingung zu beweisen, dass ∫dQ/T ≦ 0 ist, muss also vergeblich sein. Man sieht, dass dieser Schluss viel Verlockendes an sich hat und dass man ihn geradezu als ein interessantes Sophisma bezeichnen muss.",
  "translation_note": "Our translation: \"Every attempt to prove from the nature of bodies and the law of action of the forces between them, without bringing in the initial condition, that ∫dQ/T ≤ 0 must therefore be in vain. One sees that this conclusion has much that is seductive about it and that one must call it downright an interesting sophism.\" (ours)",
  "confidence_note": "Visually verified (top of p. 70). The integral is a displayed formula in the original; rendered inline here."
 },
 {
  "id": "boltzmann1877a-probability-reply",
  "author": "Ludwig Boltzmann",
  "work": "Ludwig Boltzmann, \"Bemerkungen über einige Probleme der mechanischen Wärmetheorie\", Section II: \"Über die Beziehung eines allgemeinen mechanischen Satzes zum zweiten Hauptsatze der Wärmetheorie\"",
  "year": 1877,
  "venue": "Sitzungsberichte der kaiserlichen Akademie der Wissenschaften, math.-naturw. Classe, Bd. 75, II. Abtheilung (Jahrgang 1877), pp. 62-100 (Section II = pp. 67-73). Submitted at the session of 11 January 1877.",
  "page": "pp. 70-71",
  "url_fetched": "https://viewer.acdh.oeaw.ac.at/viewer/image/MN_2Abt_75_1877/75/",
  "file_saved": "research/arrow-of-time/sources/page_images/MN_2Abt_75_1877_canvas075.jpg ; research/arrow-of-time/sources/OAW_WienerBer_75_II_1877_Boltzmann_Bemerkungen_pp62-100_tesseract.txt",
  "lang": "de",
  "verbatim": "Ein Beweis, dass nach Verlauf einer gewissen Zeit t₁ die Mischung der Kugeln mit absoluter Nothwendigkeit eine gleichförmige sein müsse, wie immer die Zustandsvertheilung zu Anfang der Zeit gewesen sein mag, kann nicht geliefert werden. Dies lehrt schon die Wahrscheinlichkeitsrechnung selbst; denn jede noch so ungleichförmige Zustandsvertheilung ist, wenn auch im höchsten Grade unwahrscheinlich, doch nicht absolut unmöglich. Ja es ist klar, das jede einzelne gleichförmige Zustandsvertheilung, welche bei einem bestimmten Anfangszustande nach Verlauf einer bestimmten Zeit entsteht, gerade so unwahrscheinlich ist wie eine einzelne noch so ungleichförmige Zustandsvertheilung, gerade so wie im Lottospiele jede einzelne Quinterne ebenso unwahrscheinlich ist wie die Quinterne 1, 2, 3, 4, 5. Nur daher, dass es viel mehr gleichförmige als ungleichförmige Zustandsvertheilungen gibt, stammt die grössere Wahrscheinlichkeit, dass die Zustandsvertheilung mit der Zeit gleichförmig wird. Man kann also nicht beweisen, dass, wie immer die Positionen und Geschwindigkeiten der Kugeln zu Anfang gewesen sein mögen, nach Verlauf einer sehr langen Zeit die Vertheilung immer gleichförmig sein muss, sondern bloss, dass unendlich vielmal mehr Anfangszustände nach Verlauf einer bestimmten längeren Zeit zu einer gleichförmigen, als zu einer ungleichförmigen Zustandsvertheilung führen und dass auch im letzteren Falle nach Verlauf einer noch längeren Zeit die Zustandsvertheilung wieder gleichförmig wird. Der Loschmidt’sche Satz lehrt also bloss Anfangszustände kennen, welche wirklich nach Verlauf einer bestimmten Zeit t₁ zu einer höchst ungleichförmigen Zustandsvertheilung führen; liefert aber nicht den Beweis, dass nicht unendlich vielmal mehr Anfangsbedingungen nach Verlauf derselben Zeit t₁ zu einer gleichförmigen führen würden. Ja im Gegentheile dies letztere folgt sogar aus dem Satze selbst, denn, da es unendlich vielmal mehr gleichförmige als ungleichförmige Zustandsvertheilungen gibt, so muss auch die Zahl der Zustände, welche nach Verlauf einer gewissen Zeit t₁ auf gleichförmige Vertheilungen folgen, viel grösser sein als die Zahl derjenigen, welche auf ungleichförmige folgen, und die letzteren sind ja nach Loschmidt als Anfangsbedingungen zu wählen, wenn sich nach der Zeit t₁ eine ungleichförmige Zustandsvertheilung einstellen soll.",
  "translation_note": "Our translation: \"A proof that after the lapse of a certain time t₁ the mixture of the spheres must with absolute necessity be uniform, whatever the distribution of states at the beginning may have been, cannot be given. This is taught by probability theory itself; for every distribution of states, however non-uniform, is, although in the highest degree improbable, not absolutely impossible. Indeed it is clear that every single uniform distribution which arises from a definite initial state after a definite time is just as improbable as a single distribution however non-uniform, just as in the lottery every single quintet is as improbable as the quintet 1, 2, 3, 4, 5. Only from the fact that there are many more uniform than non-uniform distributions does the greater probability stem that the distribution becomes uniform with time. One therefore cannot prove that, whatever the positions and velocities of the spheres at the beginning, the distribution must always be uniform after a very long time, but only that infinitely many more initial states lead after a definite longer time to a uniform than to a non-uniform distribution, and that even in the latter case the distribution will become uniform again after a still longer time. Loschmidt's theorem therefore only teaches us about initial states which really lead after a certain time t₁ to a highly non-uniform distribution; but it does not prove that infinitely many more initial conditions would not lead after the same time t₁ to a uniform one. On the contrary, this latter even follows from the theorem itself: since there are infinitely many more uniform than non-uniform distributions, the number of states that follow after a certain time t₁ upon uniform distributions must also be much greater than the number of those that follow upon non-uniform ones, and it is the latter that, according to Loschmidt, are to be chosen as initial conditions if a non-uniform distribution is to arise after the time t₁.\" (ours)",
  "confidence_note": "p. 71 visually verified against the page image (first sentence is the last sentence of p. 70, OCR, verified in the p. 70 image crop only for layout). \"das jede\" (for \"dass jede\") is as printed. Subscript 1 in t₁ as printed."
 },
 {
  "id": "boltzmann1877a-improbable-and-importance",
  "author": "Ludwig Boltzmann",
  "work": "Ludwig Boltzmann, \"Bemerkungen über einige Probleme der mechanischen Wärmetheorie\", Section II: \"Über die Beziehung eines allgemeinen mechanischen Satzes zum zweiten Hauptsatze der Wärmetheorie\"",
  "year": 1877,
  "venue": "Sitzungsberichte der kaiserlichen Akademie der Wissenschaften, math.-naturw. Classe, Bd. 75, II. Abtheilung (Jahrgang 1877), pp. 62-100 (Section II = pp. 67-73). Submitted at the session of 11 January 1877.",
  "page": "pp. 71-72",
  "url_fetched": "https://viewer.acdh.oeaw.ac.at/viewer/image/MN_2Abt_75_1877/76/",
  "file_saved": "research/arrow-of-time/sources/page_images/MN_2Abt_75_1877_canvas076.jpg ; research/arrow-of-time/sources/OAW_WienerBer_75_II_1877_Boltzmann_Bemerkungen_pp62-100_tesseract.txt",
  "lang": "de",
  "verbatim": "Man könnte sogar aus dem Verhältnisse der Zahl der verschiedenen Zustandsvertheilungen deren Wahrscheinlichkeit berechnen, was vielleicht zu einer interessanten Methode der Berechnung des Wärmegleichgewichtes führen würde. Genau analog verhält es sich mit dem zweiten Hauptsatze. [...] Da nun unendlich vielmal mehr gleichförmige als ungleichförmige Zustandsvertheilungen existiren, so ist der letztere Fall ausserordentlich unwahrscheinlich und für die Praxis kann er als unmöglich angesehen werden; geradeso wie es als unmöglich betrachtet werden kann, dass zu Anfang in einem Gefässe Sauerstoff und Stickstoff derart gemischt gewesen seien, dass nach Verlauf eines Monats der Sauerstoff sich chemisch rein in der unteren, der Stickstoff in der obern Hälfte ansammelt, was nach der Wahrscheinlichkeitsrechnung nur äusserst unwahrscheinlich aber nicht unmöglich ist. Es scheint mir trotzdem der Loschmid’sche Satz von grosser Wichtigkeit zu sein, weil er zeigt, wie innig der zweite Hauptsatz mit der Wahrscheinlichkeitsrechnung in Verbindung steht, während der erste von ihr ganz unabhängig ist. In allen Fällen, wo ∫dQ/T negativ sein kann, sind auch einzelne sehr unwahrscheinliche Anfangsbedingungen möglich, bei denen es positiv ist; und der Beweis, dass es fast immer negativ sein wird, kann nur durch Wahrscheinlichkeitsrechnung geführt werden.",
  "translation_note": "Our translation: \"One could even calculate the probability of the various state distributions from the ratio of their numbers, which might lead to an interesting method of calculating thermal equilibrium. It is exactly analogous with the second law. [...] Since there are infinitely many more uniform than non-uniform distributions, the latter case is extraordinarily improbable and can be regarded as impossible for practical purposes; just as it can be regarded as impossible that oxygen and nitrogen were initially so mixed in a vessel that after a month the oxygen collects chemically pure in the lower half and the nitrogen in the upper half, which according to probability theory is merely extremely improbable, but not impossible. Nevertheless Loschmidt's theorem seems to me of great importance, because it shows how intimately the second law is connected with probability theory, whereas the first law is entirely independent of it. In all cases where ∫dQ/T can be negative, there are also possible individual, very improbable initial conditions for which it is positive; and the proof that it will almost always be negative can only be given by probability theory.\" (ours)",
  "confidence_note": "Visually verified against page images of pp. 71 and 72. \"Loschmid’sche\" (without t) is as printed on p. 72 (typo in original). The omitted [...] sentence (p. 72) says that in some special cases it has been shown that ∫dQ/T is negative when a system passes from a non-uniform to a more uniform distribution, positive in the reverse case."
 },
 {
  "id": "boltzmann1877a-past",
  "author": "Ludwig Boltzmann",
  "work": "Ludwig Boltzmann, \"Bemerkungen über einige Probleme der mechanischen Wärmetheorie\", Section II: \"Über die Beziehung eines allgemeinen mechanischen Satzes zum zweiten Hauptsatze der Wärmetheorie\"",
  "year": 1877,
  "venue": "Sitzungsberichte der kaiserlichen Akademie der Wissenschaften, math.-naturw. Classe, Bd. 75, II. Abtheilung (Jahrgang 1877), pp. 62-100 (Section II = pp. 67-73). Submitted at the session of 11 January 1877.",
  "page": "pp. 72-73",
  "url_fetched": "https://viewer.acdh.oeaw.ac.at/viewer/image/MN_2Abt_75_1877/76/ and https://viewer.acdh.oeaw.ac.at/viewer/image/MN_2Abt_75_1877/77/",
  "file_saved": "research/arrow-of-time/sources/page_images/MN_2Abt_75_1877_canvas076.jpg ; research/arrow-of-time/sources/OAW_WienerBer_75_II_1877_Boltzmann_Bemerkungen_pp62-100_tesseract.txt",
  "lang": "de",
  "verbatim": "Noch einer eigenthümlichen Consequenz des Loschmidt’schen Satzes will ich hier Erwähnung thun, nämlich dass, wenn wir die Zustände des Weltalls in unendlich ferne Vergangenheit verfolgen, wir im Grunde genommen ebenso berechtigt sind als sehr wahrscheinlich anzunehmen, dass wir zu einem Zustande gelangen werden, in welchem endlich alle Temperaturdifferenzen aufgehört haben, als wenn wir die Zustände des Weltalles in fernste Zukunft verfolgen.",
  "translation_note": "Our translation: \"I will mention here one more peculiar consequence of Loschmidt's theorem, namely that if we follow the states of the universe into the infinitely distant past, we are fundamentally just as justified in assuming it very probable that we shall arrive at a state in which all temperature differences have finally ceased, as when we follow the states of the universe into the most distant future.\" (ours)",
  "confidence_note": "Visually verified (p. 72). Section II ends on p. 73 with the remark that relegating the second law to probability theory may make its application to the whole universe appear \"höchst bedenklich\" (OCR, p. 73)."
 },
 {
  "id": "boltzmann1877b-opening",
  "author": "Ludwig Boltzmann",
  "work": "Ludwig Boltzmann, \"Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung, respective den Sätzen über das Wärmegleichgewicht\"",
  "year": 1877,
  "venue": "Sitzungsberichte der kaiserlichen Akademie der Wissenschaften, math.-naturw. Classe, Bd. 76, II. Abtheilung (Jahrgang 1877), pp. 373-435.",
  "page": "pp. 373-374",
  "url_fetched": "https://viewer.acdh.oeaw.ac.at/viewer/image/MN_2Abt_76_1877/377/ and https://viewer.acdh.oeaw.ac.at/viewer/image/MN_2Abt_76_1877/378/",
  "file_saved": "research/arrow-of-time/sources/ocr_tesseract/MN_2Abt_76_1877_canvas377.txt ; research/arrow-of-time/sources/ocr_tesseract/MN_2Abt_76_1877_canvas378.txt ; research/arrow-of-time/sources/OAW_WienerBer_76_II_1877_Boltzmann_Beziehung_pp373-435_tesseract.txt",
  "lang": "de",
  "verbatim": "Noch klarer tritt der Zusammenhang zwischen dem zweiten Hauptsatze und den Sätzen über Wärmegleichgewicht hervor durch die Entwicklungen im II. Abschnitte meiner „Bemerkungen über einige Probleme der mechanischen Wärmetheorie“. Daselbst habe ich auch zuerst die Möglichkeit einer ganz eigenthümlichen Berechnungsweise des Wärmegleichgewichtes erwähnt, und zwar mit folgenden Worten: „Es ist klar, dass jede einzelne gleichförmige Zustandsvertheilung, welche bei einem bestimmten Anfangszustande nach Verlauf einer bestimmten Zeit entsteht, ebenso unwahrscheinlich ist, wie eine einzelne noch so ungleichförmige Zustandsvertheilung, gerade so wie im Lottospiele jede einzelne Quinterne ebenso unwahrscheinlich ist, wie die Quinterne 12345. [...]“ [...] Es ist also damit ausgesprochen, dass man den Zustand des Wärmegleichgewichtes dadurch berechnen kann, dass man die Wahrscheinlichkeit der verschiedenen möglichen Zustände des Systems aufsucht. Der Anfangszustand wird in den meisten Fällen ein sehr unwahrscheinlicher sein, von ihm wird das System immer wahrscheinlicheren Zuständen zueilen, bis es endlich den wahrscheinlichsten, d.h. den des Wärmegleichgewichtes, erreicht hat.",
  "ocr_raw": "... hervor «dureh die Entwicklungen im II. Abschnitte meiner „Bemerkungen über einige Probleme der mechanischen Wärmetheorie«. Daselbst habe ich auch zuerst die Möglichkeit einer ganz eigenthümlichen Berechnungsweise des Wärmegleiehgewichtes ... Zustanäsvertheilung ... die: Wahrseheinlichkeit ... E : immer wahrscheinlicheren Zuständen zueilen, bis es endlich den E wahrscheinlichsten ...",
  "translation_note": "Our translation: \"The connection between the second law and the theorems on thermal equilibrium emerges still more clearly through the developments in Section II of my 'Remarks on some problems of the mechanical theory of heat'. There I also first mentioned the possibility of a quite peculiar method of calculating thermal equilibrium, in the following words: 'It is clear that every single uniform distribution ... is just as improbable as a single distribution however non-uniform, just as in the lottery every single quintet is as improbable as the quintet 12345. [...]' [...] It is thus stated that one can calculate the state of thermal equilibrium by finding the probability of the various possible states of the system. The initial state will in most cases be a very improbable one; from it the system will hasten towards ever more probable states until it finally reaches the most probable, i.e. that of thermal equilibrium.\" (ours)",
  "confidence_note": "Tesseract OCR of the OAW page images, corrected only for obvious OCR noise; NOT line-by-line visually proof-read (images saved in page_images/). IMPORTANT: this paper does not name Loschmidt anywhere: our OCR of all 63 pages (pp. 373-435) contains no occurrence of \"Loschmidt\" (or \"Losch\"). The opening refers to the reversal objection only indirectly, by pointing to Section II of the \"Bemerkungen\" (the reply to Loschmidt) and quoting it."
 },
 {
  "id": "anecdote-kac1959",
  "author": "Mark Kac",
  "work": "Probability and Related Topics in Physical Sciences (Lectures in Applied Mathematics, vol. 1; proceedings of the Summer Seminar, Boulder, Colorado, 23 June - 19 July 1957), ch. III \"Probability in Classical Statistical Mechanics\"",
  "year": 1959,
  "venue": "New York / London: Interscience Publishers, 1959",
  "page": "p. 61",
  "url_fetched": "https://archive.org/download/probability-and-related-topics-in-physical-sciences/Probability%20and%20Related%20Topics%20in%20Physical%20Sciences_djvu.txt ; page image https://archive.org/download/probability-and-related-topics-in-physical-sciences/page/leaf72_w1200.jpg",
  "file_saved": "research/arrow-of-time/sources/archiveorg_Kac_1959_Probability_and_Related_Topics_djvu.txt ; research/arrow-of-time/sources/page_images/Kac1959_p61_leaf72.jpg",
  "lang": "en",
  "verbatim": "This was the earliest objection to Boltzmann’s approach and was first voiced by Loschmidt in 1876 (it is usually referred to as the “reversibility paradox”). Loschmidt simply pointed out that if a gas starting from some initial state S₀ reaches after time t a state Sₜ then presumably, Hₜ ≤ H₀. Now reverse all the velocities; then on the one hand after time t, Sₜ will come back to S₀, and on the other hand Boltzmann’s H-theorem would still yield H₀ ≤ Hₜ. Thus H could not change. (To this objection Boltzmann reportedly replied “go ahead, reverse them!”)",
  "translation_note": "n/a (English)",
  "confidence_note": "Visually verified against the page image of p. 61. Kac gives no source for the remark and flags it as hearsay (\"reportedly\"). This is the EARLIEST printed occurrence we could actually see. Later works found via archive.org full-text search (snippets only; items are lending-restricted): W. E. Parry, Many-body problems (1969): \"...reversal were pointed out to Boltzmann he reportedly replied, ‘Go ahead, reverse them.’\"; The Study of Time (Fraser et al. eds, Springer 1972): \"...a gas he is reputed to have said: “Go ahead, reverse them”\"; P. C. W. Davies, The Physics of Time Asymmetry (UC Press ed. 1977): \"(in the words of Boltzmann: ‘Go ahead, reverse them’)\"; S. Omohundro, Geometric Perturbation Theory in Physics (1986) explicitly cites \"[Kac, 1959] p. 62\" for it; H. Price, Time's Arrow and Archimedes' Point (1996): \"...which tradition attributes to Boltzmann: “Go ahead and reverse them!” he is supposed to have said.\" Page numbers for these later works were not obtainable."
 },
 {
  "id": "anecdote-boltzmann1895-memorial",
  "author": "Ludwig Boltzmann",
  "work": "\"Zur Erinnerung an Josef Loschmidt\" (memorial address, 1895), reprinted in Populäre Schriften",
  "year": 1895,
  "venue": "Ludwig Boltzmann, Populäre Schriften (Leipzig: J. A. Barth, 1905), no. 15, pp. 228ff.",
  "page": "p. 231 (Populäre Schriften, 1905)",
  "url_fetched": "https://archive.org/download/populreschrifte01boltgoog/populreschrifte01boltgoog_djvu.txt",
  "file_saved": "research/arrow-of-time/sources/archiveorg_Boltzmann_PopulaereSchriften_1905_populreschrifte01boltgoog_djvu.txt",
  "lang": "de",
  "verbatim": "Da der II. Hauptsatz von dieser Seite unangreifbar schien, versuchte es Loschmidt mit anderen Mitteln. Viel beschäftigte ihn die Idee des Umkehrens alles Geschehens, die von Professor Mach durch die Geschichte des Krebses im Mohriner See so drastisch illustriert wurde, der zwar noch nicht den Weltlauf aber bis heute schon wiederholt die Köpfe zahlreicher theoretischer Physiker in Verwirrung brachte.",
  "ocr_raw": "... versuchte es Loschmidt mit anderen Mitteln. Viel beschäftigte ihn die Idee des Umkehrens alles Geschehens, die von Professor Mach durch die Geschichte des Krebses im Mohrin er See so drastisch illustriert wurde ...",
  "translation_note": "Our translation: \"Since the second law seemed unassailable from that side, Loschmidt tried other means. He was much occupied with the idea of the reversal of all events, which Professor Mach illustrated so drastically with the story of the crab in the Mohrin lake [a reference to Mach's tale; we have not checked Mach], which, while it has not yet confused the course of the world, has to this day repeatedly confused the heads of numerous theoretical physicists.\" (ours)",
  "confidence_note": "Archive.org OCR (Google scan), \"Mohrin er\" joined. Relevance to the anecdote: this is Boltzmann's own reminiscence of Loschmidt, in which he explicitly retells joking remarks (\"Scherzworte\") from their Vienna days (the Maxwell-demon-like beings, Stefan's quip about the failed glass-tube experiment) - but it contains NO \"go ahead and reverse them\" retort. Page number from OCR running head \"Zur Erinnerung an Josef Loschmidt, 231\"; not checked against an image."
 },
 {
  "id": "levesque-verlet-1993-citation",
  "author": "D. Levesque and L. Verlet",
  "work": "\"Molecular dynamics and time reversibility\"",
  "year": 1993,
  "venue": "Journal of Statistical Physics 72 (3-4), 519-537 (issue dated August 1993). DOI 10.1007/BF01048022",
  "page": "pp. 519-537",
  "url_fetched": "https://api.crossref.org/works/10.1007/BF01048022",
  "file_saved": "research/arrow-of-time/sources/crossref_levesque_verlet_doi.json ; research/arrow-of-time/sources/crossref_levesque_verlet.json",
  "lang": "en",
  "verbatim": "[no verbatim text obtained: Crossref record has no abstract; Springer, ADS and ResearchGate returned bot-challenge/403/405 pages; Semantic Scholar says the abstract is elided by the publisher]",
  "translation_note": "n/a",
  "confidence_note": "Citation details confirmed via Crossref. A web-search summary (NOT a verified quotation, do not quote) describes the abstract as presenting \"a time-symmetrical integer arithmetic algorithm\" for MD of classical fluids, used to illustrate that time-asymmetric evolutions are typical for many-particle systems with reversible microscopic dynamics, and to compute the long-time tail of the velocity autocorrelation function. Treat as unverified until the abstract is read directly."
 },
 {
  "id": "zermelo-1896-citation",
  "author": "E. Zermelo",
  "work": "\"Ueber einen Satz der Dynamik und die mechanische Wärmetheorie\"",
  "year": 1896,
  "venue": "Annalen der Physik (Wiedemann's Annalen, Neue Folge) 57, 485-494 (1896); Crossref lists it as Annalen der Physik vol. 293, issue 3 (continuous numbering). DOI 10.1002/andp.18962930314",
  "page": "pp. 485-494",
  "url_fetched": "https://api.crossref.org/works?query.bibliographic=Zermelo+Ueber+einen+Satz+der+Dynamik+und+die+mechanische+W%C3%A4rmetheorie&rows=3",
  "file_saved": "research/arrow-of-time/sources/crossref_zermelo.json",
  "lang": "de",
  "verbatim": "[citation only]",
  "translation_note": "n/a",
  "confidence_note": "Crossref confirms title, author, pages 485-494, year 1896, DOI. The volume number \"57\" is the Wiedemann N.F. number; Crossref/Wiley use 293."
 },
 {
  "id": "rein-tamayo-2018-on-levesque-verlet",
  "author": "Hanno Rein and Daniel Tamayo",
  "work": "JANUS: a bit-wise reversible integrator for N-body dynamics",
  "year": 2018,
  "venue": "MNRAS 473, 3351 (arXiv:1704.07715)",
  "page": "Sec. 2.1 and 2.2 (arXiv PDF)",
  "url_fetched": "https://arxiv.org/pdf/1704.07715",
  "file_saved": "janus.txt",
  "lang": "en",
  "verbatim": "Levesque & Verlet (1993) presented the first integrator for molecular dynamics that is time-reversible bit by bit. The Levesque-Verlet integrator uses the position vectors at times tn−1 and tn to generate new position vectors at time tn+1",
  "translation_note": "n/a",
  "confidence_note": "pdf text extraction; used because the 1993 paper itself could not be read. Also Sec 2.2: 'After multiplying the force with the timestep squared, we convert (round) from floating point numbers to the nearest integer on our grid.'"
 }
]