Covariant Statistical Mechanics and the Stress-Energy Tensor

F. Becattini
Phys. Rev. Lett. 108, 244502 – Published 12 June 2012

Abstract

After recapitulating the covariant formalism of equilibrium statistical mechanics in special relativity and extending it to the case of a nonvanishing spin tensor, we show that the relativistic stress-energy tensor at thermodynamical equilibrium can be obtained from a functional derivative of the partition function with respect to the inverse temperature four-vector β. For usual thermodynamical equilibrium, the stress-energy tensor turns out to be the derivative of the relativistic thermodynamic potential current with respect to the four-vector β, i.e., Tμν=Φμ/βν. This formula establishes a relation between the stress-energy tensor and the entropy current at equilibrium, possibly extendable to nonequilibrium hydrodynamics.

  • Received 30 January 2012

DOI:https://doi.org/10.1103/PhysRevLett.108.244502

© 2012 American Physical Society

Authors & Affiliations

F. Becattini

  • Università di Firenze and INFN Sezione di Firenze, Florence, Italy

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Issue

Vol. 108, Iss. 24 — 15 June 2012

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