Tolman-Ehrenfest effect for an ideal gas in a background of time-independent electric, magnetic, and gravitational fields

The statistical mechanics of an ideal gas of point particles moving in a time independent background metric with $g_{0j}\ne 0$ is investigated. An explicit calculation shows that when there is no background electrostatic or magnetostatic field the thermodynamic pressure, energy density, and thermally averaged energy-momentum tensor depend on temperature and chemical potential only through the ratios $T_0/\sqrt{g_{00}}$ and ${\mu }_0/\sqrt{g_{00}}$. A background magnetostatic field does not change this, however with a background electrostatic field the previous results are multiplied by a factor $\exp (-e{A}_0/T_0)$, which is an exception to the strict Tolman-Ehrenfest rule because the system is open.