Maximum configuration principle for driven systems with arbitrary driving

TL;DR

This paper develops a maximum configuration entropy framework for driven dissipative systems, enabling a statistical and thermodynamic description of non-equilibrium processes with arbitrary driving, using sample space reducing processes as a model.

Contribution

It introduces a novel entropy functional for driven systems with memory, extending the maximum configuration principle to non-equilibrium, arbitrarily driven dissipative processes.

Findings

Derived the entropy functional for driven systems with memory.

Established a Legendre structure for driven non-equilibrium systems.

Provided a framework for a statistical thermodynamic theory of driven processes.

Abstract

Depending on context, the term entropy is used for a thermodynamic quantity, a~measure of available choice, a quantity to measure information, or, in the context of statistical inference, a maximum configuration predictor. For systems in equilibrium or processes without memory, the mathematical expression for these different concepts of entropy appears to be the so-called Boltzmann--Gibbs--Shannon entropy, H.For processes with memory, such as driven- or self-reinforcing-processes, this is no longer true: the different entropy concepts lead to distinct functionals that generally differ from H. Here we focus on the maximum configuration entropy (that predicts empirical distribution functions) in the context of driven dissipative systems. We develop the corresponding framework and derive the entropy functional that describes the distribution of observable states as a function of the details of the driving process. We do this for sample space reducing (SSR) processes, which provide an analytically tractable model for driven dissipative systems with controllable driving. The fact that a consistent framework for a maximum configuration entropy exists for arbitrarily driven non-equilibrium systems opens the possibility of deriving a full statistical theory of driven dissipative systems of this kind. This provides us with the technical means needed~to derive a thermodynamic theory of driven processes based on a statistical theory. We discuss the Legendre structure for driven systems.