Steady state thermodynamics of ideal gas in shear flow

TL;DR

This paper develops a thermodynamic-like framework to describe the energy exchange and stable states of an ideal gas under shear flow, extending equilibrium thermodynamics concepts to non-equilibrium steady states.

Contribution

It introduces a steady-state thermodynamics approach for ideal gases in shear flow, deriving a fundamental relation and an extremum principle for stability.

Findings

Derived a fundamental relation between internal energy and state parameters.

Postulated an extremum principle for stable steady states.

Analyzed a non-equilibrium transition in shear flow.

Abstract

Equilibrium thermodynamics describes the energy exchange of a body with its environment. Here, we describe the global energy exchange of an ideal gas in the Coutte flow in a thermodynamic-like manner. We derive a fundamental relation between internal energy as a function of parameters of state. We analyze a non-equilibrium transition in the system and postulate the extremum principle, which determines stable stationary states in the system. The steady-state thermodynamic framework resembles equilibrium thermodynamics.