Nonequilibrium Thermodynamics of Spacetime

Abstract

It has previously been shown that the Einstein equation can be derived from the requirement that the Clausius relation dS = δQ/T hold for all local acceleration horizons through each spacetime point, where dS is one quarter the horizon area change in Planck units, and δQ 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 = δQ/T + diS, where diS 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.

Bouncing universe with modified dispersion relation

“…Recently, this scenario has been extensively investigated in various approaches [38][39][40][41][42][43][44][45][46][47][48]. In particular, based on the assumption that the gravitational theory can be described by entropy force [49], which has been widely interested by many theorists [40,[50][51][52][53][54][55][56][57][58][59][60][61][62][63], the authors in [40] proposed that an interesting setup was that the modified dispersion relation prevented the energy density of the matter contents from diverging at high energy level such that the modified Friedmann equation with the bouncing effect can be derived successfully from the Clausius relation, where the singularity of the corresponding spacetime was free.…”

On the holographic basis of loop quantum cosmology

“…Such an interpretation of spacetime was later reinforced by Padmanabhan, who linked the macroscopic description of spacetime, by Einstein equations, to microscopic degrees of freedom when assuming the principle of equipartition of energy [35]. A further extension of the Jacobson results to non-equilibrium situations has also been done [36]. The Jacobson's results have given rise to several works which have strengthened the thermodynamic interpretation of Einstein's equations.…”

Study of GSLT in Curvature-Matter Coupling Gravity

“…Akbar and Cai [2] found that Friedmann equations evaluated at the apparent horizon can be rewritten in the form dE = τdS + WdV (E, τ, S , V and W are the energy, temperature, entropy, volume inside the horizon and work density, respectively) in the background of GR, GaussBonnet (GB) gravity and the general Lovelock theory. It is found that an auxiliary entropy production term corresponding to the non-equilibrium treatment of thermodynamics is appeared in Clausius relation in modied theories of gravity while no such additional term is obtained in braneworld, GB and Lovelock gravitational theories [3]. Wu et al [4] formulated the universal condition to check the validity of generalized second law of thermodynamics (GSLT) in the context of modied theories of gravity.…”