Non-equilibrium thermodynamics of small-scale systems

TL;DR

This paper explores how non-equilibrium thermodynamics applies to small-scale systems, highlighting the influence of fluctuations and finite-size effects, and deriving mesoscopic thermodynamic equations for such systems.

Contribution

It demonstrates that non-equilibrium thermodynamics remains valid at small scales and formulates a mesoscopic thermodynamics framework incorporating fluctuations and finite-size effects.

Findings

Non-equilibrium thermodynamics applies to small systems.

Finite-size effects significantly influence system dynamics.

Mesoscopic thermodynamic equations are derived.

Abstract

Small thermodynamic systems exhibit peculiar behavior different from that observed in long-scale systems. Non-equilibrium processes taking place in those systems are strongly influenced by the presence of fluctuations which can be large. Contributions to the free energy which vanish at the infinite number of particles limit cannot be neglected and may exert an important influence on the dynamics. We show that in spite of these important differences, the method of non-equilibrium thermodynamics still applies when reducing the size of the system. By using this method, assumption of local equilibrium at the mesoscale thereby leads to the formulation of a mesoscopic nonequilibrium thermodynamics from which expressions for the non-equilibrium currents and kinetic equations for the probability density can be obtained.