Statistical mechanics of reparametrization-invariant systems. It takes three to tango

Understand

It is notoriously difficult to apply statistical mechanics to generally covariant systems, because the notions of time, energy and equilibrium are seriously modified in this context.

• We discuss the conditions under which weaker versions of these notions can be defined, sufficient for statistical mechanics.
• We focus on reparametrization-invariant systems without additional gauges.
• The key is to reconstruct statistical mechanics from the ergodic theorem.