Speaker
Description
The connection between gravity and thermodynamics provides a profound perspective on the nature of spacetime dynamics. Jacobson famously demonstrated that the Einstein field equations can be derived by assuming the Bekenstein--Hawking relation, in which the entropy is proportional to the area of local Rindler horizons, within the framework of equilibrium thermodynamics. However, when this entropy--area relation is modified, non-equilibrium thermodynamic contributions become essential. For instance, when spacetime curvature explicitly enters this relation, the resulting field equations reduce to the $f(R)$ class of modified gravity. In this work, we address the question: \emph{what are the gravitational field equations arising from the most general entropy--area relation?} Employing non-equilibrium thermodynamic formalism, we derive the corresponding field equations for an arbitrary functional dependence $S = \alpha f(A)$. As a concrete application, we examine the case of Tsallis entropy, characterized by the non-additivity parameter $\delta$. We show that the resulting cosmological equations---comprising the two Friedmann-like equations and a new non-equilibrium constraint---constitute an overdetermined system for any value $\delta \neq 1$. The only mathematically self-consistent solution corresponds to $\delta \equiv 1$, which exactly recovers the standard $\Lambda$CDM model. Our results thus demonstrate that, contrary to previous claims based on incomplete equilibrium approaches, Tsallis cosmology does not provide a dynamically consistent alternative to standard cosmology when non-equilibrium effects are properly taken into account.
