The open system has been proved to be a system with perfect accessibility represented as a probability space in which is defined a PA-measure. But, the PA-measure is not yet known; consequently, it is difficult to develop the statistical thermodynamics for an irreversible system. Here its...

An increasing number of natural phenomena appear to deviate from standard statistical distributions. It has kindled interest in alternative formulation of statistical mechanics which should preserve most of the mathematical structures of the Boltzmann–Gibbs theory, while reproducing the...