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A Comparison Of Boltzmann And Gibbs Definitions Of Microcanonical Entropy For Small Systems, Randall B. Shirts

Faculty Publications

Two different definitions of entropy, S= klnW, in the microcanonical ensemble have been competing for over 100 years. The Boltzmann/Planck definition is that W is the number of states accessible to the system at its energy E (also called the surface entropy). The Gibbs/Hertz definition is that W is the number of states of the system up to the energy E (also called the volume entropy). These two definitions agree for large systems but differ by terms of order N^-1 for small systems, where N is the number of particles in the system. For three analytical …