Thermodynamics of Dissipative Solitons

TL;DR

This paper draws an analogy between dissipative solitons in nonlinear systems and thermodynamic systems, describing their properties and energy limits through thermodynamic concepts like temperature and entropy.

Contribution

It introduces a thermodynamic framework for dissipative solitons, highlighting their quasi-particle nature and energy scaling limits in mode-locked lasers.

Findings

Dissipative solitons behave like bounded quasi-particles with thermodynamic properties.

Energy scaling of dissipative solitons is limited by coherence loss and thermalization.

The thermodynamic analogy explains the generation and limitations of chirped pulses in lasers.

Abstract

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 an incoherent ``basin.'' We demonstrate the main limits of the dissipative soliton energy scaling which result from the loss of internal soliton coherency and the thermalization due to nontriviality of a ``free energy landscape.''