Non-equilibrium distribution function in ultra-fast processes

TL;DR

This paper introduces a simple model for non-equilibrium distribution functions in ultra-fast processes, deriving thermodynamic relations and identifying conditions for classical and non-equilibrium regimes, validated by inertial heat conduction law.

Contribution

It proposes a novel expression for non-equilibrium distribution functions based on temporal derivatives, extending thermodynamic relationships to ultra-fast processes.

Findings

Derived the law of inertial heat conduction.

Identified the threshold between slow and fast processes.

Revealed two types of pressure in non-equilibrium.

Abstract

A simple expression for the non-equilibrium distribution function in ultra-fast transient processes is proposed. Postulating its dependence on temporal derivatives of the equilibrium integrals of motion, non-equilibrium analogues of the thermodynamic relationships are derived and the conditions that maximize the non-equilibrium entropy are identified. A rigorous threshold between ``slow" and ``fast" processes is suggested, identifying the range of applicability of classical quasi-equilibrium description. The proposed theory is validated by deriving the known law of inertial heat conduction, which accounts for finite speed of thermal propagation. Finally, a new expression for the non-equilibrium work is derived, revealing two kinds of pressure that emerge in fast non-equilibrium.