General relativistic statistical mechanics
Understanding thermodynamics and statistical mechanics in the fully general relativistic context is an open problem. I give tentative definitions of equilibrium state, mean values, mean geometry, entropy and temperature, which reduce to the conventional ones in the nonrelativistic limit but remain valid for a general covariant theory. The formalism extends to quantum theory. The construction builds on the idea of thermal time, on a notion of locality for this time, and on the distinction between global and local temperature. The last is the temperature measured by a local thermometer and is given by $kT=\ensuremath{\hbar}d\ensuremath{\tau}/ds$, with $k$ the Boltzmann constant, $\ensuremath{\hbar}$ the Planck constant, $ds$ proper time and $d\ensuremath{\tau}$ the equilibrium thermal time.