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

Résumé fourni par la source

Thermodynamic reasoning has entered nonlinear optics along three routes—wave-turbulence kinetics, the equilibrium thermodynamics of highly multimoded systems, and the statistical mechanics of mode locking—but in each the modal basis or coarse-graining cutoff is specified externally, by a waveguide, a spectral window, or a cavity bandwidth. This review asks what survives when the object is a strongly chirped dissipative soliton of the complex cubic–quintic Ginzburg–Landau equation, a structure that exists only because energy flows through it. The mechanism that localizes such a pulse also bounds its spectrum, separating the correlation function into a graining scale set by the spectral cutoff and a collective scale set by the spectral core. Their ratio is selected by the dynamics rather than imposed, and closed-form adiabatic spectra in both dispersion regimes compress the parameter space onto a single master diagram carrying a shape entropy, an internal energy, and a continuation-dependent energy–entropy slope. Dissipative soliton resonance is read as spectral core narrowing, intrinsic in normal dispersion and conditional in anomalous dispersion. We state precisely where the borrowed vocabulary becomes strained: a deterministic pulse remains first-order coherent, so the scale ratio is not yet a count of statistical degrees of freedom, and the promotion requires an ensemble-coherence calibration that is specified but not assumed. The result is a falsifiable framework for dissipative-soliton coherence, energy scaling, and stability, with experimental signatures and design criteria for chirped-pulse oscillators.

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