- Open Access
Modified Unruh thermodynamics in emergent gravity: Finite heat capacity and Rényi entropy
Phys. Rev. Research 8, 013260 – Published 9 March, 2026
DOI: https://doi.org/10.1103/mnm4-mylh
Abstract
We show that Jacobson's thermodynamic derivation of Einstein's equations remains valid when local Rindler horizons are modeled as finite heat-capacity systems, resolving the infinite-bath assumption of Unruh thermodynamics. The horizon entropy then takes the form of Rényi entropy with nonextensivity parameter , or equivalently an “Einstein entropy” that uniquely preserves Einstein's equations for arbitrary . In both cases, the Unruh temperature is modified to , establishing a universal link between finite-capacity thermodynamics and generalized entropies. We further derive a corrected scalar Einstein equation with an upper bound on horizon energy flux, suggesting testable signatures in heavy-ion collisions, spin-polarization experiments, and analog gravity, emergent gravity.
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