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We show that the generalized Boltzmann distribution is the only distributionfor which the Gibbs-Shannon entropy equals the thermodynamic entropy. Thisresult means that the thermodynamic entropy and the Gibbs-Shannon entropy arenot generally equal, but rather than the equality holds only in the specialcase where a system is in equilibrium with a reservoir.

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