Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung resp. den Sätzen über das Wärmegleichgewicht

Boltzmann, Ludwig; Hasenöhrl, Friedrich

doi:10.1017/cbo9781139381437.011

Cited by 181 publications

(269 citation statements)

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“…Boltzmann's entropy is consistent with the second law of thermodynamics [8][9][10]. It is easy to see for the example given above that the change in Boltzmann's entropy is zero when a container of milk is partitioned.…”

Section: Boltzmann's Definition Of the Entropysupporting

confidence: 60%

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Gibbs’ Paradox and the Definition of Entropy

Swendsen

2008

Entropy

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Gibbs' Paradox is shown to arise from an incorrect traditional definition of the entropy that has unfortunately become entrenched in physics textbooks. Among its flaws, the traditional definition predicts a violation of the second law of thermodynamics when applied to colloids. By adopting Boltzmann's definition of the entropy, the violation of the second law is eliminated, the properties of colloids are correctly predicted, and Gibbs' Paradox vanishes.

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Section: Boltzmann's Definition Of the Entropysupporting

confidence: 60%

“…Boltzmann defined the entropy in terms of the probability of the macroscopic state of a composite system [8][9][10]. Although the traditional definition of the entropy is often attributed to Boltzmann, this attribution is not correct.…”

Section: Boltzmann's Definition Of the Entropymentioning

confidence: 99%

Gibbs’ Paradox and the Definition of Entropy

Swendsen

2008

Entropy

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“…On a probability measure that assigns probabilities to regions of phase space that are proportional to their phase-space volume, entropy is then connected with probability. In this section we follow the procedure of Boltzmann (1877bBoltzmann ( , 1995, which is summarized in Ehrenfest and Ehrenfest (1912). For simplicity, we consider a system that consists of a large number N of identical molecules, each with r degrees of freedom (the generalization to systems consisting of several types of molecules is straightforward).…”

Section: Basic Concepts Of Hamiltonian Dynamicsmentioning

confidence: 99%

Probabilities in Statistical Mechanics

Myrvold

2017

Oxford Handbooks Online

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This chapter reviews selected aspects of the terrain of discussion of the role of probabilities in statistical mechanics. Among the topics addressed are the reasons for introduction of probabilities into statistical mechanics, the status of the standard equilibrium distribution, and the question of interpretation of statistical mechanical probabilities. The chapter starts with a brief history of probabilities in physics and the evolution of statistical mechanics therefrom. The approaches of Boltzmann and Gibbs are presented, and then some approaches to justifying choice of probability measures. The chapter closes with a presentation of possible resolutions to some puzzling aspects of the use of standard probability measures.

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“…This measure, which we denote S H , describes the dispersion of microstates, and does not involve any macroscopic variables. A third concept, which we denote S W , links macroscopic with microscopic descriptions; it was defined by Boltzmann (1877), and is proportional to the logarithm of the number of microstates consistent with a given macroscopic state. (This measure of entropy was introduced in population genetics by Barton (1989) and Barton and Rouhani (1993) Suppose that a polygenic trait is approximately normally distributed.…”

Section: Application To Quantitative Geneticsmentioning

confidence: 99%