Proof of entropy principle in Einstein-Maxwell theory

Abstract

We consider a static self-gravitating charged perfect fluid system in the Einstein-Maxwell theory. Assume Maxwell's equation and the Einstein constraint equation are satisfied, and the temperature of the fluid obeys Tolman's law. Then we prove that the total entropy of the fluid achieves an extremum implies other components of Einstein's equation for any variations of metric and electrical potential with fixed boundary values. Conversely, if Einstein's equation and Maxwell's equations hold, the total entropy achieves an extremum. Our work suggests that the maximum entropy principle is consistent with Einstein's equation when electric field is taken into account.

LaTex, 16 pages, some minor changes and simplified derivations, references added, matches published version

References in corpus (4)

• Maximum Entropy Principle for Self-gravitating Perfect Fluid in Lovelock Gravity
• Is gravity entropic force?
• General proof of (maximum) entropy principle in Lovelock gravity
• Stationarity of Extremum Entropy Fluid Bodies in General Relativity

Cited by in corpus (6)

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• Thermodynamical stability for perfect fluid
• Consistency between dynamical and thermodynamical stabilities for perfect fluid in $f(R)$ theories
• Thermodynamic equilibrium condition and the first law of thermodynamics for charged perfect fluids in electromagnetic and gravitational fields
• Consistency between dynamical and thermodynamical stabilities for charged self-gravitating perfect fluid
• Universality of entropy principle for a general diffeomorphism-covariant purely gravitational theory