The mesoscopic dynamics of thermodynamic systems

TL;DR

This paper discusses recent advances in extending thermodynamic concepts into mesoscopic and irreversible regimes using probabilistic methods, enabling analysis of complex non-equilibrium systems.

Contribution

It introduces a systematic approach to derive stochastic dynamics from equilibrium properties via Fokker-Planck equations, broadening thermodynamics' applicability.

Findings

Applicable to non-linear transport with potential barriers

Models activated processes and slow relaxation phenomena

Analyzes biomolecular processes like translocation and stretching

Abstract

Concepts of everyday use like energy, heat, and temperature have acquired a precise meaning after the development of thermodynamics. Thermodynamics provides the basis for understanding how heat and work are related and with the general rules that the macroscopic properties of systems at equilibrium follow. Outside equilibrium and away from macroscopic regimes most of those rules cannot be applied directly. Here we present recent developments that extend the applicability of thermodynamic concepts deep into mesoscopic and irreversible regimes. We show how the probabilistic interpretation of thermodynamics together with probability conservation laws can be used to obtain Fokker-Planck equations for the relevant degrees of freedom. This approach provides a systematic method to obtain the stochastic dynamics of a system directly from its equilibrium properties. A wide variety of situations can be studied in this way, including many that were thought to be out of reach of thermodynamic theories, such as non-linear transport in the presence of potential barriers, activated processes, slow relaxation phenomena, and basic processes in biomolecules, like translocation and stretching.