Maximum entropy generation and κκ-exponential model

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 phenomenology of the anomalous systems. The κκ-theory has obtained a lot of results in the analysis of natural phenomena, but it was not extended to irreversible open systems. A modified κκ-theory is proposed for its use in irreversible open systems.