Statistical mechanics of reparametrization invariant systems. Takes Three to Tango

Abstract : 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 idea is to reconstruct statistical mechanics from the ergodic theorem. We find that a suitable split of the system into two non-interacting components is sufficient for generalizing statistical mechanics. While equilibrium acquires sense only when the system admits a suitable split into three weakly interacting components ---roughly: a clock and two systems among which a generalization of energy is equi-partitioned. The key property that allows the application of statistical mechanics and thermodynamics is an additivity condition of such generalized energy.
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Contributor : Carlo Rovelli <>
Submitted on : Monday, January 18, 2016 - 9:30:22 PM
Last modification on : Thursday, March 15, 2018 - 4:56:08 PM

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  • HAL Id : hal-01258359, version 1
  • ARXIV : 1503.08725

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Thibaut Josset, Goffredo Chirco, Carlo Rovelli. Statistical mechanics of reparametrization invariant systems. Takes Three to Tango. Classical and Quantum Gravity, IOP Publishing, 2016, 33, pp.045005. ⟨hal-01258359⟩

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