A non-equilibrium theoretical framework for statistical physics with application to turbulent systems and their predictability

TL;DR

This paper introduces a new variational framework for non-equilibrium statistical physics, extending to turbulent systems and autonomous dynamics, and offers methods for analyzing predictability and calculating thermodynamical trajectories.

Contribution

It develops a generalized variational approach applicable to a wide range of non-equilibrium systems, including turbulence and autonomous dynamics, enhancing predictability analysis and numerical trajectory computation.

Findings

Extended the theoretical framework to autonomous systems.

Provided a method for analyzing predictability limits in turbulence.

Outlined a numerical approach for far-from-equilibrium trajectories.

Abstract

A new theoretical approach to non-equilibrium statistical systems has recently been proposed by the author, a co-author and others. It is based on a variational principle which is associated with the discrepancy of a path through thermodynamical space to one following Liouvillean evolution. In this contribution the approach is extended in such a way that it can be applied to a wide range of practical non-equilibrium statistical systems such as those arising in turbulence but also to a general class of statistical physics models. The new methodology allows for application to autonomous dynamical systems generalizing the previous work which applied only to Hamiltonian systems. Furthermore it provides a general analysis of near equilibrium conditions which allows for a natural analysis of predictability limits in turbulent systems. Finally it describes a method is described for the numerical calculation of far from equilibrium thermodynamical trajectories.