Thermodynamic Equilibrium of a Wormhole Station

We study the thermodynamic equilibrium of a station which connects many distinct asymptotic regions of a space-time. An example of the station is a throat of a wormhole connecting two asymptotic regions. The temperatures of the station measured in various asymptotic regions are not necessarily the same. We propose a conjecture relating the temperatures in a coordinate independent manner and present explicit examples which support the conjecture. We also suggest a fundamental question on the identity of mass.