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“…However, in his famous treatment of kinetic theory of gases, Boltzmann gave proof of the H-theorem [ 15 , 16 , 17 ], which can be interpreted as the 2nd law of thermodynamics for ideal gases in any state. Entropy and its balance follow directly by integration from the particle distribution function and the Boltzmann equation, and there is no limitation at all to equilibrium states.…”

confidence: 99%

“…However, in his famous treatment of kinetic theory of gases, Boltzmann gave proof of the H-theorem [ 15 , 16 , 17 ], which can be interpreted as the 2nd law of thermodynamics for ideal gases in any state. Entropy and its balance follow directly by integration from the particle distribution function and the Boltzmann equation, and there is no limitation at all to equilibrium states.…”

confidence: 99%

“…According to the studies of standard statistical mechanics, it seems reasonable although not mandatory to choose f ( x | y ) as Maxwellian distribution . However, f ( y ) is usually unknown, even we suppose that f ( y ) is known, the input parameters in f ( y ) may very hard to be determined.…”

confidence: 99%

“…With known distribution function (Eq. ) and other proper modifications, we can have a complete statistical mechanics for mesoscience following the general procedure of standard statistical mechanics …”

confidence: 99%

“…It is assumed that the mean free path of the near-independent particles is larger than the size of the filter, and the interaction among particles is neglected inside the energy filter. Therefore, according to the Boltzmann equation [38], the particle flux flowing out of the hot/cold reservoir per unit time can be expressed as…”

confidence: 99%