Death and resurrection of the zeroth principle of thermodynamics

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.

Figure 1

Typical overlap between $\psi (0)$ and $\psi (t)$ as a function of time.

Figure 2

A phase-space region moves from one cell to next in the time ${\tau }_0\sim h/\Delta E$.