Death and resurrection of the zeroth principle of thermodynamics

TL;DR

This paper revisits the zeroth principle of thermodynamics, proposing a generalized informational approach that remains valid in relativistic gravity, linking temperature to quantum state distinguishability and information flow.

Contribution

It introduces a new derivation of temperature uniformity at equilibrium based on quantum information theory, applicable in relativistic contexts.

Findings

Temperature uniformity relates to equal distinguishable quantum state transitions.

Net information flow between systems vanishes at equilibrium.

The approach extends thermodynamics principles to relativistic and quantum regimes.

Abstract

The zeroth principle of thermodynamics in the form "temperature is uniform at equilibrium" is notoriously violated in relativistic gravity. Temperature uniformity is often derived from the maximization of the total number of microstates of two interacting systems under energy exchanges. Here we discuss a generalized version of this derivation, based on informational notions, which remains valid in the general context. The result is based on the observation that the time taken by any system to move to a distinguishable (nearly orthogonal) quantum state is a universal quantity that depends solely on the temperature. At equilibrium the net information flow between two systems must vanish, and this happens when two systems transit the same number of distinguishable states in the course of their interaction.