title: Covariant statistical mechanics and the stress-energy tensor.
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., T(μν)=-∂Φ(μ)/∂β(ν). This formula establishes a relation between the stress-energy tensor and the entropy current at equilibrium, possibly extendable to nonequilibrium hydrodynamics.
authors.affiliation: Università di Firenze and INFN Sezione di Firenze, Florence, Italy.
authors.forename: F
authors.initials: F
authors.lastname: Becattini