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.