耗散孤子的热力学框架：从光子学到湍流及玻色-爱因斯坦凝聚类比
Toward a Thermodynamic Framework for Dissipative Solitons: From Photonics to Turbulence and Bose--Einstein Condensate Analogies
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中文总结 AI 辅助
本研究构建耗散孤子的热力学框架，探究其尺度分离指数的统计意义，分析不同色散下的特性，形成适用于啁啾脉冲振荡器的理论框架。
中文摘要 AI 辅助
非线性光学中的统计推理遵循三条路径：波湍流动力学、多模平衡热力学、锁模统计力学，三者均依赖外部指定的模态基（波导、光谱窗口或腔带宽）。本文探究复三次-五次金兹堡-朗道方程的耗散孤子（DS）是否能提供动态选择的内部尺度比作为粗粒化变量。DS会生成自身的光谱尺度：局域化约束光谱，定义细粒化尺度（截止值）和集体核心尺度；其动态选择的比值定义了涌现的尺度分离指数，该指数仅在系综相干校准后才作为有效模数获得统计意义，这是本研究的核心创新点。闭式绝热光谱将各 regime 压缩至含熵、内能及能量-熵斜率的主图中。DSR（耗散孤子共振）表现为光谱核心变窄，在正常色散中为固有特性，在反常色散中为条件特性。沿正常色散方向，熵代理量的交叉先于单脉冲损失，暗示多脉冲选择，但噪声驱动的转变有待验证；沿反常色散方向无转变（路径依赖）。有限时间噪声揭示存在区域内存在单侧可达边界，其作用仍待探究。确定性脉冲保持相干，该比值并非自由度计数；熵分解不唯一，温度斜率非状态函数，熵多脉冲选择为推测性结论，各限定条件均可测试。本文还概述了与波湍流、孤子气体、玻色-爱因斯坦凝聚（BEC）及负温度态的对比，最终形成了详述 DS 相干性、稳定性、标度性的紧凑框架，为啁啾脉冲振荡器提供了实验特征与设计准则。
英文摘要
# 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.
