On the Entropy of Relaxing Deterministic Systems
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In this paper, we re-visit Gibbs' second (unresolved) paradox, namely the constancy of the fine-grained Gibbs entropy for autonomous Hamiltonian systems. We compare and contrast the different roles played by dissipation and entropy both at equilibrium where dissipation is identically zero and away from equilibrium where entropy cannot be defined and seems unnecessary in any case. Away from equilibrium dissipation is a powerful quantity that can always be defined and that appears as the central argument of numerous exact theorems: the fluctuation, relaxation, and dissipation theorems and the newly derived Clausius inequality.
The Journal of Chemical Physics
Thermodynamics and Statistical Physics
Transport Properties and Non-Equilibrium Processes
Statistical Mechanics in Chemistry