Thermodynamics of arbitrary spherical surfaces in FLRW spacetimes
In this work, we investigate the thermodynamics of arbitrary spherically symmetric surfaces in non-flat FLRW spacetimes within general relativity. Adopting the gravity-to-thermodynamics perspective, the Clausius relation and the unified first law follow directly from the gravitational field equations and matter dynamics, with a central role played by the matter-flux measure derived from energy-momentum conservation. The cosmological apparent-horizon and event-horizon thermodynamics are both recovered as special cases. In particular, the event-horizon temperatures derived from the gravitational dynamics satisfy both thermodynamic relations without introducing phenomenological modifications, and the corresponding temperature reduces to the Gibbons-Hawking temperature in the de Sitter limit. We further show that previous inconsistencies originate from incompatible temperature prescriptions rather than from any intrinsic deficiency in the thermodynamics of the cosmological event horizon. These results demonstrate that the gravity-thermodynamics correspondence is a generic feature of gravitational dynamics rather than a property unique to causal horizons.