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

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arXiv:2403.18652v1 Announce Type: new
Abstract: The statistical mechanics of an ideal gas of point particles moving in a time independent background metric with $g_{0j}\neq 0$ 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 $\exp(-eA_{0}/T_{0})$, which is an exception to the strict Tolman-Ehrenfest rule because the system is open.

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