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.
Versions
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BibTeX
@misc{kalashnikov2026toward,
title = {{Toward a Thermodynamic Framework for Dissipative Solitons: From Photonics to Turbulence and Bose--Einstein Condensate Analogies}},
author = {Vladimir L. Kalashnikov and Irina T. Sorokina},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.10510},
eprint = {2608.10510},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.10510},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Toward a Thermodynamic Framework for Dissipative Solitons: From Photonics to Turbulence and Bose--Einstein Condensate Analogies
AU - Vladimir L. Kalashnikov
AU - Irina T. Sorokina
PY - 2026
DA - 2026/08/18
PB - arXiv
DO - 10.48550/arxiv.2608.10510
UR - https://arxiv.org/abs/2608.10510
AB - # 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.
ER -