On Equivalence of Nonequilibrium Thermodynamic and Statistical Entropies

Entropy

关键词: Thermodynamic entropy;    statistical entropy;    second law of thermodynamics;    reversible and irreversuible processes;    macro- and micro-states;    internal variables;    state;    state variables;    state function;    internal equilibrium;    homogeneous and inhomogeneous states;    temporal and ensemble averages;    phase space confinement;    vitrification and residual entropy;    Gibbs and Boltzmann formulations;    negative entropy;   

DOI  :  10.3390/e17020710

来源: mdpi

【 摘 要 】

We review the concept of nonequilibrium thermodynamic entropy and observables and internal variables as state variables, introduced recently by us, and provide a simple first principle derivation of additive statistical entropy, applicable to all nonequilibrium states by treating thermodynamics as an experimental science. We establish their numerical equivalence in several cases, which includes the most important case when the thermodynamic entropy is a state function. We discuss various interesting aspects of the two entropies and show that the number of microstates in the Boltzmann entropy includes all possible microstates of non-zero probabilities even if the system is trapped in a disjoint component of the microstate space. We show that negative thermodynamic entropy can appear from nonnegative statistical entropy.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland