Optical Entropy and Generalized Thermodynamics of Solitonic Event Horizons

TL;DR

The paper develops a nonequilibrium thermodynamic framework for optical solitonic event horizons by defining an operational entropy through spectral partitioning into a coherent soliton (horizon) and an incoherent radiative bath. It demonstrates that resonant radiation emitted when third-order dispersion breaks soliton integrability acts as the primary entropy carrier, and that the total coarse-grained entropy $S_{\mathrm{tot}} = S_{\mathrm{hor}} + S_{\mathrm{rad}}$ satisfies a generalized second law, $\frac{d S_{\mathrm{tot}}}{d\xi} \ge 0$, during soliton fission. Numerical simulations of the generalized nonlinear Schrödinger equation confirm monotonic entropy growth and reveal nonperturbative scaling of radiation with dispersion, $I_{\mathrm{rad}} \propto \exp(-1/\delta_3)$, and a thermal tail in the radiation spectrum with $|\tilde{\psi}(k)|^2 \propto \exp(-k/\kappa_{\mathrm{eff}})$ leading to an effective Hawking temperature $T_H \approx 150\ \mathrm{K}$. The results position optical horizons as genuine nonequilibrium thermodynamic systems and provide a practical route to quantify information entropy in laboratory analog gravity experiments, linking horizon dynamics, integrability breaking, and thermodynamics in driven photonic media.

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 Schrodinger equation confirm that this process satisfies a generalized second law, where the change in total entropy is non-negative. These results establish optical event horizons as consistent nonequilibrium thermodynamic systems, offering a new pathway to explore the information-theoretic aspects of analog gravity in laboratory settings.

Figures (2)

• Figure 1: Spectral partitioning and entropy density of the optical horizon system. (a) Bipartite decomposition of the instantaneous field spectrum into a localized soliton component (system) and a dispersive radiation component (bath). The shaded regions define the frequency domains $\Omega_S$ and $\Omega_R$ used in the operational entropy measures. (b) Spectral entropy density $-p(\omega)\ln p(\omega)$ evaluated over the radiation domain $\Omega_R$, highlighting the dominant contribution of resonant dispersive modes to entropy generation.
• Figure 2: Thermodynamic signatures of a solitonic optical event horizon. (a) Spectral evolution $|\tilde{\psi}(k,\xi)|^2$ showing a localized soliton core and the emission of dispersive resonant radiation induced by integrability-breaking higher-order dispersion, defining a natural system–bath partition. (b) Evolution of the total coarse-grained entropy $S_{\mathrm{tot}}=S_{\mathrm{hor}}+S_{\mathrm{rad}}$. Despite local fluctuations due to finite coarse-graining, the entropy exhibits a non-decreasing trend consistent with a generalized second law. (c) High-frequency tail of the radiation spectrum displaying exponential decay, $|\tilde{\psi}(k)|^2 \propto e^{-k/\kappa_{\mathrm{eff}}}$, indicating thermal statistics that emerge concomitantly with entropy production and are governed by an effective surface gravity.