First law of thermodynamics on holographic screens in entropic force frame

Abstract

Imposing a mathematical definition of holographic screen, in the spirit of Verlindeʼs entropic force proposal (E.P. Verlinde, arXiv:1001.0785), we give the differential and integral form of the first law of thermodynamics on the holographic screen enclosing a spherical symmetric black hole. It is consistent with equipartition principle and the form of Komar mass. There are also other version of first law, which are equivalent up to a Legendre transformation. The holographic screen thermodynamics is defined in a quasi-local form, which is the main difference to black hole thermodynamics. Thus, the physical interpretation of holographic screen thermodynamics might be different from black hole thermodynamics. We argue that the entropy of the holographic screen determines its area, i.e. S=A4. And the metric can be expressed by thermodynamics variables, which is an illustration of how the space is foliated by the thermodynamical potentials.