Physics
Scientific paper
Oct 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997phdt........31d&link_type=abstract
Thesis (PhD). THE UNIVERSITY OF CHICAGO, Source DAI-B 58/04, p. 1922, Oct 1997, 36 pages.
Physics
Scientific paper
Boltzmann's 1872 derivation of the H-theorem was of great significance because it provided a basis for the second law of thermodynamics in terms of the molecular/kinetic theory of heat. By showing that a statistical treatment of the many molecules comprising a gas can produce a monotonic decrease of an entropy-like quantity, H /propto [-]S, he provided the essential insight into the connection between the second law and the evolution of systems through macroscopic states occupying progressively larger volumes in phase space. However, it is a common misconception that an analysis like that given by Boltzmann demonstrates that the second law of thermodynamics would be observed in a universe of particles whose motions are completely described by the laws of classical mechanics. I attempt to clarify that this is a misconception by showing that an element introduced into Boltzmann's derivation as simply an approximation to the dynamics expected under classical mechanics, in fact introduces a new feature into the dynamics of the model system. It is shown that this added feature, present in the model but not in a classical mechanical universe, is solely responsible for the monotonic behavior of H. Hence, while this type of analysis provides an understanding of how the second law comes about, it does not stay within the confines of classical mechanics in doing so. Thus it is not a derivation of the second law of thermodynamics just from the laws of classical mechanics for a system with many degrees of freedom and a low-entropy initial condition. The implications of this conclusion are important for our understanding of the physical basis of the second law of thermodynamics.
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