Statistical mechanics of covariant systems with multi-fingered time

TL;DR

This paper extends a covariant statistical mechanics framework to systems with multiple Hamiltonian constraints, demonstrating the recovery of known relativistic effects and distributions within a multi-fingered time approach.

Contribution

It generalizes previous covariant statistical mechanics to multi-fingered time systems, clarifying the role of interactions in defining equilibrium.

Findings

Recovered Ehrenfest-Tolman effect in multi-fingered framework

Derived Jüttner distribution for relativistic gas covariantly

Highlighted the importance of interactions for global equilibrium

Abstract

Recently, in [Class. Quantum Grav. 33 (2016) 045005], the authors proposed a new approach extending the framework of statistical mechanics to reparametrization-invariant systems with no additional gauges. In this work, the approach is generalized to systems defined by more than one Hamiltonian constraints (multi-fingered time). We show how well known features as the Ehrenfest- Tolman effect and the J\"uttner distribution for the relativistic gas can be consistently recovered from a covariant approach in the multi-fingered framework. Eventually, the crucial role played by the interaction in the definition of a global notion of equilibrium is discussed.