On Non-Equilibrium Thermodynamics of Space–Time and Quantum Gravity

Abstract

Based on recent results from general relativistic statistical mechanics and black hole information transfer limits a space-time entropy-action equivalence is proposed as a generalization of the holographic principle. With this conjecture, the action principle can be replaced by the second law of thermodynamics, and for the Einstein-Hilbert action the Einstein field equations are conceptually the result of thermodynamic equilibrium. For non-equilibrium situations Jaynes' information-theoretic approach to maximum entropy production is adopted instead of the second law of thermodynamics. As it turns out, for appropriate choices of constants quantum gravity is obtained. For the special case of a free particle the Bekenstein-Verlinde entropy-to-displacement relation of holographic gravity, and thus the traditional holographic principle, emerges. Although Jacobson's original thermodynamic equilibrium approach proposed that gravity might not necessarily be quantized, this particular non-equilibrium treatment might require it.