文档介绍：Boltzmann’s Approach to Statistical Mechanics
Sheldon Goldstein
Departments of Mathematics and Physics
Rutgers University
Piscataway NJ 08854, USA
Abstract. In the last quarter of the eenth 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 inno-
vations – 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.
1 Introduction
I shall focus here on Boltzmann’s approach to the problem of the arrow of time:
the origin of irreversible macroscopic laws, ., and most importantly, the second
law of thermodynamics – the law of increasing entropy – in the reversible laws
of microscopic physics. I shall assume, as of course did Boltzmann, a classical
framework, for the most part ignoring quantum mechanics.
As a matter of fact, it is widely believed that the transition from classical me-
chanics to quantum mechanics requires no essential modification of Boltzmann’s
ideas. This may well be so, but I believe that the traditional formulation of
quantum theory is much too vague to permit any definitive conclusions on this
matter. (For a non-traditional formulation of quantum mechanics that avoids
its conceptual incoherence, a formulation which I quite naturally believe is well
worth very serious consideration, see the contribution of Detlef Durr¨ to this
volume.)
For a more detailed presentation of much of what is discussed here, the reader
should consult the excellen