A General Maximum Entropy Principle for Self-Gravitating Perfect Fluid

  • Sijie GaoEmail author
Part of the Springer Proceedings in Physics book series (SPPHY, volume 170)


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.


Einstein Equation Spherical Symmetry Perfect Fluid Total Entropy Hydrostatic Equilibrium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This research was supported by NSFC Grants No. 11235003, 11375026 and NCET-12-0054.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of PhysicsBeijing Normal UniversityBeijingChina

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