Developments in the foundations of statistical mechanics during the past ten years or so. The author discusses how statistical concepts enter the treatment of deterministic mechanical systems, with particular reference to trajectory instabilities and to the KAM theorem. Then he deals with large systems: the thermodynamic limit and the theory of infinite systems. Non-equilibrium statistical mechanics is covered but LC relativistic statistical mechanics is not.

https://iopscience.iop.org/article/10.1088/0034-4885/42/12/002/pdf

Foundations of statistical mechanics

Translation of Ludwig Boltzmann’s Paper “On the Relationshipbetween the Second Fundamental Theorem of the MechanicalTheory of Heat and Probability Calculations Regarding theConditions for Thermal Equilibrium” Sitzungberichte derKaiserlichen Akademie der Wissenschaften.Mathematisch-Naturwissen Classe. Abt. II, LXXVI 1877, pp373-435 (Wien. Ber. 1877, 76:373-435). Reprinted in Wiss.Abhandlungen, Vol. II, reprint 42, p. 164-223, Barth, Leipzig,1909

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Translation of Ludwig Boltzmann's Paper "On the Relationship between the Second Fundamental Theorem of the Mechanical Theory of Heat and Probability Calculations Regarding the Conditions for Thermal Equilibrium" Sitzungberichte der Kaiserlichen Akademie der Wissenschaften.

Translation of the seminal 1877 paper by Ludwig Boltzmann which for the first time established the probabilistic basis of entropy. Includes a scientific commentary.

https://www.mdpi.com/1099-4300/17/4/1971/pdf

Translation of Ludwig Boltzmann's Paper ``On the Relationship between the Second Fundamental Theorem of the Mechanical Theory of Heat and Probability Calculations Regarding the Conditions for Thermal Equilibrium'' Sitzungberichte der Kaiserlichen Akademie der Wissenschaften. Mathematisch-Naturwissen Classe. Abt. II, LXXVI 1877, pp 373-435 (Wien. Ber. 1877, 76:373-435). Reprinted in Wiss. Abhandlungen, Vol. II, reprint 42, p. 164-223, Barth, Leipzig, 1909

The dependence of the entropy on the number of molecules can never be found from studying closed systems The argument based on counting states of particles, indistinguishable or not, is therefore spurious On the other hand, interaction with particle reservoirs leads to different results for distinguishable and indistinguishable molecules The choice between both depends on whether the experimentalist is able and willing to make the distinction, not on the fundamental properties of the molecules Thus the paradox is resolved by replacing the Platonic idea of entropy with an operational definition Quantum mechanics has no bearing on the question

The Gibbs Paradox

Dem Zweck dieser Sammlung entsprechend soll in dem folgenden Artikel nicht ein Uberblick uber die gesamte Leistung des Nernstschen Warmesatzes (NW) in den 25 Jahren seines Bestehens2 gegeben, sondern vielmehr geschildert werden, wie wir ihn heute nach den Fortschritten der letzten Jahre ansehen. Fur diesen Uberblick erscheint der gegenwartige Zeitpunkt — auch abgesehen vom auseren Anlas — recht geeignet, da Theorie und Experiment jetzt den Zusammenhang mit den allgemeinen quantentheoretischen Gesetzen klar erkennen lassen.

V. Trakal

Papers

Ableitung des Dissoziationsgleichgewichtes aus der Quantentheorie und darauf beruhende Berechnung der chemischen Konstanten