The mathematics of the ensemble theory

This study shows that the generalized Boltzmann distribution is only mathematically consistent with thermodynamics when system described by an ensemble of a certain mathematical form. form very general, such canonical, grand-canonical, or isothermal–isobaric theories are all special cases this Compared standard textbook formalism statistical mechanics (SM), approach does not require prior distribution, assume functional maximization entropy, and employs fewer assumptions. Therefore, new insight challenges belief on requirement in SM provides way to derive distribution. also reveals logical constraints SM’s fundamental components; therefore, it could potentially benefit researchers non-Boltzmann–Gibbs philosophers studying foundations SM.