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It is notoriously difficult to apply statistical mechanics to generallycovariant systems, because the notions of time, energy and equilibrium areseriously modified in this context. We discuss the conditions under whichweaker versions of these notions can be defined, sufficient for statisticalmechanics. We focus on reparametrization-invariant systems without additionalgauges. The key is to reconstruct statistical mechanics from the ergodictheorem. We find that a suitable split of the system into two non interactingcomponents is sufficient for generalizing statistical mechanics. Whileequilibrium acquires sense only when the system admits a suitable split intothree weakly interacting components ---roughly: a clock and two systems amongwhich a generalization of energy is equi-partitioned. This allows theapplication of statistical mechanics and thermodynamics as an additivitycondition of such generalized energy.

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