A General Maximum Entropy Principle for Self-Gravitating Perfect Fluid
We consider a self-gravitating system consisting of perfect fluid in a spherically symmetric spacetime. Using the Gibbs-Duhem relation, we extremize the total entropy S under the constraints that the total number and energy of particles are fixed. We show that the extrema of S coincides precisely with the relativistic Tolman-Oppenheimer-Volkoff (TOV) equation of hydrostatic equilibrium. Furthermore, we show that the maximum entropy principle is also valid for a charged perfect fluid. Our work provides a strong evidence for the fundamental relationship between general relativity and ordinary thermodynamics.
KeywordsEinstein Equation Spherical Symmetry Perfect Fluid Total Entropy Hydrostatic Equilibrium
This research was supported by NSFC Grants No. 11235003, 11375026 and NCET-12-0054.