Non-equilibrium Thermodynamics of Spacetime

TL;DR

This paper extends the thermodynamic derivation of Einstein's equations to include non-equilibrium effects and curvature corrections, introducing entropy production terms related to bulk and shear viscosities of horizons.

Contribution

It introduces a non-equilibrium framework for deriving gravitational field equations with curvature-dependent entropy corrections, incorporating entropy production from viscosity effects.

Findings

Curvature corrections require non-equilibrium treatment.

Entropy production terms relate to horizon viscosities.

Field equations include bulk viscosity contributions.

Abstract

It has previously been shown that the Einstein equation can be derived from the requirement that the Clausius relation dS = dQ/T hold for all local acceleration horizons through each spacetime point, where dS is one quarter the horizon area change in Planck units, and dQ and T are the energy flux across the horizon and Unruh temperature seen by an accelerating observer just inside the horizon. Here we show that a curvature correction to the entropy that is polynomial in the Ricci scalar requires a non-equilibrium treatment. The corresponding field equation is derived from the entropy balance relation dS =dQ/T+dS_i, where dS_i is a bulk viscosity entropy production term that we determine by imposing energy-momentum conservation. Entropy production can also be included in pure Einstein theory by allowing for shear viscosity of the horizon.