Thermodynamical stability for a perfect fluid

Abstract

According to the maximum entropy principle, it has been proved that the gravitational field equations could be derived by the extrema of the total entropy for a perfect fluid, which implies that thermodynamic relations contain information as regards gravity. In this manuscript, we obtain a criterion for the thermodynamical stability of an adiabatic, self-gravitating perfect fluid system by the second variation of the total entropy. We show, for Einstein's gravity with spherical symmetry spacetime, that the criterion is consistent with that for the dynamical stability derived by Chandrasekhar and Wald. We also find that the criterion could be applied to cases without spherical symmetry, or under general perturbations. The result further establishes the connection between thermodynamics and gravity.

Consistency between dynamical and thermodynamical stabilities for perfect fluid in f(R) theories

“…Combining with the result obtained in Ref. [24], we find that the dynamical stability can be replaced by thermodynamical stability not only in general relativity, but also in modified theories, such as f (R) theories. It suggests that there is a universal inherent connection between thermodynamics and gravity.…”

“…Please refer to Refs. [6] and [24] to obtain further details and discussion. Considering a perfect fluid star in static background spacetime with a static slice , we assume that quantities are measured by static observers.…”

“…In Ref. [24] we have shown that if the star is deviated slightly from equilibrium state, the second variation of total entropy takes the form…”

“…[24], we presented a generalized thermodynamical criterion, which is the second variation of total entropy for perfect fluid star. And we showed that in general relativity it can provide the same stability criterion as the dynamical stability criterion obtained by Wald [17].…”

Consistency between dynamical and thermodynamical stabilities for charged self-gravitating perfect fluid

“…Roupas proved that the maximum of total entropy of perfect fluid is consistent with the dynamical stability obtained by Yabushita [17,18]. More recently, we show that the dynamical stability and thermodynamical stability are exactly the same both in general relativity or some modified theory such as f (R) theories [19,20].…”