The Generalized Boltzmann Distribution is the Only Distribution in Which the Gibbs-Shannon Entropy Equals the Thermodynamic Entropy

Abstract

We show that the generalized Boltzmann distribution is the only distribution for which the Gibbs-Shannon entropy equals the thermodynamic entropy. This result means that the thermodynamic entropy and the Gibbs-Shannon entropy are not generally equal, but rather than the equality holds only in the special case where a system is in equilibrium with a reservoir.

References in corpus (3)

• Quantum Thermodynamic Cycles and quantum heat engines
• Typicality for Generalized Microcanonical Ensembles
• Quantum Heat Engine With Multi-Level Quantum Systems