Beyond Comoving Volume: Horizon Flux and Matter Creation in Entropic Cosmology

TL;DR

The paper addresses thermodynamic consistency in entropic cosmology with gravitational particle creation when the apparent horizon volume is noncomoving, modeling the horizon region as an open system. It applies the unified first law to the apparent horizon, accounting for horizon flux, and derives a generalized second law (GSL) that couples horizon and matter sectors. A key result is the explicit decomposition of the horizon's particle-number evolution into bulk production ($N_h Gamma$) and horizon-flux ($N_h 3H q$), with a creation pressure $p_c$ related to the production rate by $p_c = -(\rho+p)\,\Gamma/(3H)$ in the adiabatic case; the GSL imposes thermodynamic constraints, such as $\Gamma \gtrsim H$ for late-time acceleration with dust. These findings provide a thermodynamic foundation for matter-creation cosmologies and clarify how horizon dynamics can drive cosmic acceleration without exotic dark energy.

Abstract

We explore the derivation of the Friedmann equations from a thermodynamic perspective, applying the unified first law of thermodynamics to the apparent horizon of a flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe. We extend this framework to incorporate gravitationally induced particle creation, treating the region enclosed by the apparent horizon as an open thermodynamic system. A crucial aspect of our analysis is the recognition that the apparent horizon volume is not comoving; this requires a consistent accounting of particle exchange across the moving boundary. We demonstrate that the evolution of the particle number, and explicitly the matter entropy, can be decomposed into two distinct physical contributions: genuine bulk particle production and a net flux induced by the dynamics of the horizon itself. Finally, we derive the Generalized Second Law (GSL) in this setting, showing transparently how the total entropy budget is balanced by horizon thermodynamics, bulk creation, and boundary fluxes.