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 . 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 , i.e., . 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