Holographic Bound From Second Law of Thermodynamics

TL;DR

This paper demonstrates that the holographic bound, which limits a system’s entropy by its surface area, can be derived from the generalized second law of thermodynamics through thought experiments, supporting Susskind's claim.

Contribution

It shows that the holographic bound follows from the generalized second law for various gravitating systems, providing a thermodynamic foundation for the holographic principle.

Findings

Holographic bound derived from the second law

Supports Susskind's claim on the bound's thermodynamic origin

Applicable to both weakly and strongly gravitating systems

Abstract

A necessary condition for the validity of the holographic principle is the holographic bound: the entropy of a system is bounded from above by a quarter of the area of a circumscribing surface measured in Planck areas. This bound cannot be derived at present from consensus fundamental theory. We show with suitable {\it gedanken} experiments that the holographic bound follows from the generalized second law of thermodynamics for both generic weakly gravitating isolated systems and for isolated, quiescent and nonrotating strongly gravitating configurations well above Planck mass. These results justify Susskind's early claim that the holographic bound can be gotten from the second law.