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

Abstract

# Abstract Thermodynamic concepts are increasingly used in nonlinear photonics to describe Rayleigh--Jeans thermalization, optical wave turbulence, condensation, negative-temperature states, and statistical mode locking. This raises a broader question: how far can thermodynamic reasoning be extended to localized structures maintained far from equilibrium by a balance of gain, loss, dispersion, and nonlinearity? We address this question using strongly chirped dissipative solitons (DSs) of the complex cubic--quintic Ginzburg--Landau equation (CQGLE) 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 descriptions based on spectral entropy, internal energy, effective temperature, and condensation-like spectral restructuring, relating them to dissipative-soliton resonance (DSR), stochastic mode-locking self-start, and redistribution between single- and multipulse attractors. Normal and anomalous group-delay dispersion (NGD and AGD) provide complementary realizations: in NGD, DSR is accompanied by spectral localization, scale separation, and increasing accessibility of multipulse states; in AGD, the spectrum has extended wings and dynamical robustness occupies only part of the existence domain. These results distinguish general features of nonequilibrium state selection from effects tied to a particular localization mechanism. We argue that thermodynamic-like observables are best viewed as coarse-grained structural diagnostics rather than equilibrium state variables, while DSs provide a photonic platform linking nonequilibrium thermodynamics, wave turbulence, driven condensates, and statistical phase-transition concepts.