Covariant statistical mechanics and the stress-energy tensor

Details Covariant statistical mechanics and the stress-energy tensor Covariant statistical mechanics and the stress-energy tensor

2012-01-25

arxiv.org/abs/1201.5278v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages, 1 figure. Corrected signs in equations

Scientific paper

After recapitulating the covariant formalism of equilibrium statistical mechanics in special relativity and extending it to the case of a non-vanishing 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 \beta. 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 \beta, i.e. T^{\mu \nu} = - \partial \Phi^\mu/\partial \beta_\nu. This formula is a relativistic extension of the familiar relation between mean energy and the temperature derivative of the partition function.

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