Paths and stochastic order in open systems

TL;DR

This paper demonstrates that the maximum entropy generation principle in open systems arises from a stochastic order of paths in phase space, establishing a bidirectional relationship between path order and entropy production at stability.

Contribution

It proves that the maximum entropy generation principle results from a stochastic order of paths, linking thermodynamic stability to path ordering in phase space.

Findings

Entropy generation is maximized at stability.

The stochastic order of paths determines entropy production.

Maximum entropy generation implies a stochastic order of paths.

Abstract

The principle of maximum irreversible is proved to be a consequence of a stochastic order of the paths inside the phase space; indeed, the system evolves on the greatest path in the stochastic order. The result obtained is that, at the stability, the entropy generation is maximum and, this maximum value is consequence of the stochastic order of the paths in the phase space, while, conversely, the stochastic order of the paths in the phase space is a consequence of the maximum of the entropy generation at the stability.