Generalized Thermodynamics of Solitonic Event Horizons in Dispersive Field Theories

TL;DR

This paper develops a thermodynamic framework for solitonic event horizons in dispersive optical systems, defining entropy and demonstrating entropy production through resonant radiation emission, thus establishing a nonequilibrium thermodynamics perspective.

Contribution

It introduces an operational entropy for solitonic horizons and shows how resonant radiation mediates entropy production, extending thermodynamics to dispersive optical analogs of black holes.

Findings

Resonant radiation emission increases entropy in solitonic horizons.

Numerical simulations confirm the generalized second law holds.

Event horizons in dispersive fields are shown to be consistent nonequilibrium systems.

Abstract

The realization of Hawking radiation in optical analogs has historically focused on kinematic observables, such as the effective temperature determined by the horizon's surface gravity. A complete thermodynamic description, however, necessitates a rigorous definition of entropy and irreversibility, which has remained elusive in Hamiltonian optical systems. In this work, we bridge this gap by introducing an operational entropy for solitonic event horizons, derived from the spectral partitioning of the optical field into coherent solitonic and incoherent radiative subsystems. We demonstrate that the emission of resonant radiation -- mediated by the breaking of soliton integrability due to higher-order dispersion -- serves as a fundamental mechanism for entropy production. Numerical simulations of the generalized nonlinear Schr\"odinger equation confirm that this process satisfies a generalized second law, $\Delta S_{\mathrm{tot}} \ge 0$. These results establish event horizons in dispersive field theories as consistent nonequilibrium thermodynamic systems, offering a new pathway to explore the information-theoretic aspects of analog gravity in laboratory settings.