On the Cocycle Structure of the Boltzmann Distribution
Abstract
Based on a cocycle structure, we identify a new derivation of the Boltzmann distribution for finite energy-level systems from the maximal entropy principle (MEP). Our approach does not rely on the method of the Lagrange multiplier, and it provides a more transparent way to understand the dependence on the energy levels of the temperature T = 1/β for the equilibrium distribution. Finally, we make two curious observations associated with our derivations.
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