1201.5278 (F. Becattini)

Covariant statistical mechanics and the stress-energy tensor    [PDF]

F. Becattini

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.

View original: http://arxiv.org/abs/1201.5278