Regularized Boltzmann entropy determines macroscopic adiabatic accessibility

2016/01/04 by Hiroyasu Tajima, Eyuri Wakakuwa, Tajima, Hiroyasu +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Protein Structure and Dynamics #Statistical Mechanics and Entropy #cond-mat.mes-hall #cond-mat.stat-mech #quant-ph

paper · pdf · doi:10.48550/arxiv.1601.00487

10 pages, 1 figures

arxiv created 2016/10/02 · arxiv updated 2016/10/04

Abstract

How the thermodynamic entropy S_TD is related to the Boltzmann entropy S_B has been one of the central issues since the beginning of statistical mechanics. Today, it is believed that the thermodynamic entropy S_TD is equal to a function S_B that is defined by regularizing the Boltzman entropy in order to ensure extensivity. However, it is not known whether S_B completely determines the possibility of a macroscopic adiabatic transformation in the same way as S_TD does. In this paper, by formulating the possibility of a macroscopic adiabatic transformations in terms of "coarse-graining" of quantum operations, we prove that S_B provides a necessary and sufficient condition for the possibility of a macroscopic adiabatic transformation.

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