On the Local Equilibrium Principle

TL;DR

This paper introduces a Local Equilibrium Condition (LEC) to precisely define local equilibrium in physical systems, deriving the Unruh temperature and analyzing equilibrium states of massless quanta in various scenarios.

Contribution

It proposes a rigorous LEC framework applicable to non-interacting quanta, providing new insights into local equilibrium and phenomena like the Unruh effect and Bénard instability.

Findings

Derived the Unruh temperature using LEC.

Showed global temperature constancy for stationary spherical equilibrium.

Discovered non-trivial rotating equilibrium states with temperature gradients.

Abstract

A physical system should be in a local equilibrium if it cannot be distinguished from a global equilibrium by ``infinitesimally localized measurements''. This seems to be a natural characterization of local equilibrium, however the problem is to give a precise meaning to the qualitative phrase ``infinitesimally localized measurements''. A solution is suggested in form of a {\em Local Equilibrium Condition} (LEC) which can be applied to non-interacting quanta. The Unruh temperature of massless quanta is derived by applying LEC to an arbitrary point inside the Rindler Wedge. Massless quanta outside a hot sphere are analyzed. A stationary spherically symmetric local equilibrium does only exist according to LEC if the temperature is globally constant. Using LEC a non-trivial stationary local equilibrium is found for rotating massless quanta between two concentric cylinders of different temperatures. This shows that quanta may behave like a fluid with a B\'enard instability.