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

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.

💡 Research Summary

The paper presents a unified thermodynamic framework that brings together two previously separate lines of research in cosmology: entropic cosmology based on the apparent horizon and gravitationally induced particle creation. Starting from the flat Friedmann‑Lemaître‑Robertson‑Walker (FLRW) metric, the authors apply the unified first law of thermodynamics, (T,dS_h = -dE + W,dV), to the apparent horizon whose radius is (r_A = H^{-1}). They identify the total energy inside the horizon as (E = \rho V_h) with (V_h = \frac{4\pi}{3}r_A^3), the work density as (W = (\rho-p)/2), and adopt the Bekenstein‑Hawking entropy (S_h = \pi H^{-2}) together with the temperature set by the surface gravity. By taking time derivatives and using the standard conservation law (\dot\rho + 3H(\rho+p)=0), they recover the Friedmann equations, thereby showing that the cosmic dynamics can be interpreted as an equation of state derived from horizon thermodynamics.

A crucial point emphasized throughout the work is that the volume bounded by the apparent horizon is not comoving; it changes in time according to (\dot V_h/V_h = 3\dot r_A/r_A = 3H(1+q)), where (q = -\dot H/H^2 -1) is the deceleration parameter. This non‑comoving nature implies that even in the absence of genuine particle creation, the total particle number inside the horizon, (N_h = n V_h), can vary because particles cross the moving boundary. The authors therefore write the Gibbs relation for an open system, \