Maximum Entropy Principle for the Microcanonical Ensemble

TL;DR

This paper derives the microcanonical ensemble from the Maximum Entropy Principle using phase space volume entropy, providing an alternative to the traditional Shannon entropy approach.

Contribution

It introduces a derivation of the microcanonical ensemble based on phase space volume entropy, expanding the theoretical foundations of statistical mechanics.

Findings

Derives microcanonical ensemble from phase space volume entropy

Shows equivalence with traditional Shannon entropy approach

Provides a complementary perspective on energy constraints

Abstract

We derive the microcanonical ensemble from the Maximum Entropy Principle (MEP) using the phase space volume entropy of P. Hertz. Maximizing this entropy with respect to the probability distribution with the constraints of normalization and average energy, we obtain the condition of constant energy. This approach is complementary to the traditional derivation of the microcanonical ensemble from the MEP using Shannon entropy and assuming a priori that the energy is constant which results in equal probabilities.