Thermodynamics of Dissipative Solitons

We establish a close analogy between the thermodynamics of the nonlinear systems far from equilibrium and the dissipative solitons. Unlike the solitons in the Hamiltonian systems, their dissipative counterpart looks like an aggregation of bounded quasi-particles interacting on the short range, obeying the Rayleigh-Jeans distribution, and possessing a temperature, entropy, and other thermodynamic characteristics. This ensemble is confined by a collective potential, which defines its negative chemical potential. Such a dissipative soliton represents a strongly chirped pulse generated by a mode-locked laser with the advantage of being energy scalable by the analogy with the Bose-Einstein condensation from a noncoherent “basin.” We demonstrate the main limits of the dissipative soliton energy scaling, or the dissipative soliton resonance existence: the loss of internal soliton coherency and the thermalization due to nontriviality of a “free energy landscape”.