Elsevier

Annals of Physics

Volume 25, Issue 1, October 1963, Pages 48-90
Annals of Physics

The statistical thermodynamics of equilibrium

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Abstract

A statistical thermodynamics is developed in terms of extensive variables (additive invariants) distributed over a cellular division in space. In general, this distribution is governed by randomness and by correlations. The present theory, however, deals explicitly only with randomness, although correlations are implicit in the so-called fixed variables of the system. Because of this restriction, the theory is valid only for the fluctuations of coupled systems that have reached their equilibrium; hence we call it the statistical thermodynamics of equilibrium, briefly STE. A set of postulates is advanced, the essence of which is the requirement that distribution functions (d.f.) exist for two basic coupling situations. It is implicit that the system has a memory-loss mechanism; and the d.f. does not depend on past history (ergodic property). Such qualitative assumptions are sufficient to derive the Gibbsian d.f.'s in their quantitative form. These d.f.'s describe the coupling of finite systems with infinite environments and can be used to analyze typical situations of measurement by the methods of mathematical statistics. The present point of view sheds some new light on the ergodic problem and on the role of Nernst's law in completing the definition of thermodynamic equilibrium. An attempt is made to clarify the relations between entropy, information, and uncertainty by advancing a generic notion, the dispersal of a d.f., that subsumes these concepts as special cases.

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    This paper, which is a development of a Ph.D. Thesis (to be referred to hereafter as “Thesis”) submitted by one of the authors (PMQ) to the Department of Physics, Massachusetts Institute of Technology, August 1958, was supported in part by the U. S. Army Signal Corps, the Air Force Office of Scientific Research, and the Office of Naval Research; and in part by the U. S. Air Force (Office of Scientific Research) under ASD Contract AF 49(638)-95. Reproduction in whole or in part is permitted for any purpose of the United States Government.

    Currently on leave of absence at the Laboratoire de Chimie Physique de la Faculté des Sciences de Paris. John Simon Guggenheim Memorial Fellow.

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