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In classical statistical mechanics, the ''H''-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency to increase in the quantity ''H'' (defined below) in a nearly-ideal gas of molecules.〔 L. Boltzmann, "(Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen )." Sitzungsberichte Akademie der Wissenschaften 66 (1872): 275-370. English translation: 〕 As this quantity ''H'' was meant to represent the entropy of thermodynamics, the ''H''-theorem was an early demonstration of the power of statistical mechanics as it claimed to derive the second law of thermodynamics—a statement about fundamentally irreversible processes—from reversible microscopic mechanics. The ''H''-theorem is a natural consequence of the kinetic equation derived by Boltzmann that has come to be known as Boltzmann's equation. The ''H''-theorem has led to considerable discussion about its actual implications, with major themes being: * What is entropy? In what sense does Boltzmann's quantity ''H'' correspond to the thermodynamic entropy? * Are the assumptions (such as the ''Stosszahlansatz'' described below) behind Boltzmann's equation too strong? When are these assumptions violated? == Definition and meaning of Boltzmann's ''H'' == The ''H'' value is determined from the function ''f''(''E'',''t'') ''dE'', which is the energy distribution function of molecules at time ''t''. The value ''f''(''E'',''t'') ''dE'' is the number of molecules that have kinetic energy between ''E'' and ''E'' + ''dE''. ''H'' itself is defined as: For an isolated ideal gas (with fixed total energy and fixed total number of particles), the function ''H'' is at a minimum when the particles have a Maxwell–Boltzmann distribution; if the molecules of the ideal gas are distributed in some other way (say, all having the same kinetic energy), then the value of ''H'' will be higher. Boltzmann's ''H''-theorem, described in the next section, shows that when collisions between molecules are allowed, such distributions are unstable and tend to irreversibly seek towards the minimum value of ''H'' (towards the Maxwell–Boltzmann distribution). (Note on notation: Boltzmann originally used the letter ''E'' for quantity ''H''; most of the literature after Boltzmann uses the letter ''H'' as here. Boltzmann also used the symbol ''x'' to refer to the kinetic energy of a particle.) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「H-theorem」の詳細全文を読む スポンサード リンク
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