Toward a Thermodynamic Framework for Dissipative Solitons: From Photonics to Turbulence and Bose–Einstein Condensate Analogies

Résumé fourni par la source

Thermodynamic concepts are increasingly used in nonlinear photonics to describe Rayleigh–Jeans thermalization, optical wave turbulence, condensation, negative-temperature states, and statistical mode locking. We ask how far this reasoning can be extended to localized structures maintained far from equilibrium by gain, loss, dispersion, and nonlinearity, using strongly chirped dissipative solitons (DSs) of the complex cubic–quintic Ginzburg–Landau equation as a model system. Their internal energy flows and separation of correlation scales connect coherent solitary waves with semi-incoherent wave kinetics, driven-open systems, and Bose–Einstein-condensation analogies. We review thermodynamic-like indicators based on spectral entropy, internal energy, effective temperature, and spectral condensation, and we relate them to dissipative-soliton resonance (DSR), stochastic mode-locking self-start, and redistribution between single- and multipulse attractors. Normal and anomalous group-delay dispersion provide complementary cases. In normal dispersion, DSR is accompanied by spectral localization, increasing scale separation, and growing multipulse accessibility; the statistical degree-count interpretation becomes meaningful only after the two scales separate and still requires ensemble calibration. In anomalous dispersion, the spectrum has extended wings, and noisy calculations reveal finite robust regions inside a larger existence domain, without an analogous thermodynamic turnover along the continuation tested. Thus, the unification is strongest at the level of the adiabatic solution and state-selection diagnostics, not an equilibrium thermodynamics. DSs thereby provide a photonic platform linking nonequilibrium thermodynamics, wave turbulence, driven condensates, and statistical phase-transition concepts.

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