Boltzmann’s Approach to Statistical Mechanics
نویسنده
چکیده
In the last quarter of the nineteenth century, Ludwig Boltzmann explained how irreversible macroscopic laws, in particular the second law of thermodynamics, originate in the time-reversible laws of microscopic physics. Boltzmann’s analysis, the essence of which I shall review here, is basically correct. The most famous criticisms of Boltzmann’s later work on the subject have little merit. Most twentieth century innovations – such as the identification of the state of a physical system with a probability distribution ̺ on its phase space, of its thermodynamic entropy with the Gibbs entropy of ̺, and the invocation of the notions of ergodicity and mixing for the justification of the foundations of statistical mechanics – are thoroughly misguided.
منابع مشابه
ar X iv : c on d - m at / 0 10 52 42 11 M ay 2 00 1 Boltzmann ’ s Approach to Statistical Mechanics
In the last quarter of the nineteenth century, Ludwig Boltzmann explained how irreversible macroscopic laws, in particular the second law of thermodynamics, originate in the time-reversible laws of microscopic physics. Boltzmann’s analysis, the essence of which I shall review here, is basically correct. The most famous criticisms of Boltzmann’s later work on the subject have little merit. Most ...
متن کاملRealizing Boltzmann’s dream: computer simula- tions in modern statistical mechanics
Today, computer simulations belong to the most important and powerful theoretical tools for the investigation of statistical mechanical systems particularly in the field of condensed matter. Many simulation methods may directly, or indirectly, be traced back to ideas of Ludwig Boltzmann or are used to carry on the program he had envisioned. Using several illustrative examples, we discuss the ro...
متن کاملBoltzmann’s H-theorem, its discontents, and the birth of statistical mechanics
A comparison is made of the traditional Loschmidt (reversibility) and Zermelo (recurrence) objections to Boltzmann’s H-theorem, and its simplified variant in the Ehrenfests’ 1912 wind-tree model. The littlecited 1896 (measure-theoretic) objection of Zermelo (similar to an 1889 argument due to Poincaré) is Boltzmann’s thinking in response to the objections taken together. & 2009 Published by Els...
متن کاملBoltzmann’s H-theorem, its limitations, and the birth of (fully) statistical mechanics
A comparison is made of the traditional Loschmidt (reversibility) and Zermelo (recurrence) objections to Boltzmann’s H-theorem, and its simplified variant in the Ehrenfests’ 1912 wind-tree model. The little-cited 1896 (pre-recurrence) objection of Zermelo (similar to an 1889 argument due to Poincaré) is also analysed. Significant differences between the objections are highlighted, and several o...
متن کاملThe Road to Maxwell’s Demon Conceptual Foundations of Statistical Mechanics
Recently I reviewed the book, The Road to Maxwell’s Demon: Conceptual Foundations of Statistical Mechanics, by Meir Hemmo and Orly Shenker, in this journal (Hemmo and Shenker 2012a; Allori 2013). In that book, Hemmo and Shenker put forward their own account of statistical mechanics. They think that, since Boltzmann’s explanation fails, we are in need of such an account. While I was enthusiastic...
متن کامل