Free-energy transition in a gas of non-interacting nonlinear wave-particles

TL;DR

This paper studies phase transitions in a gas of non-interacting soliton waves, revealing that collective behavior leads to a first order phase transition characterized by shock wave formation, using exact nonlinear solutions and chaos-based statistical mechanics.

Contribution

It demonstrates that even non-interacting wave particles can exhibit critical phenomena and phase transitions through collective dynamics analyzed via exact solutions and chaos-based statistical mechanics.

Findings

Identification of a free energy metamorphosis with increasing excitation

Observation of shock wave formation as a phase transition signature

Evidence that independent degrees of freedom can sustain critical phenomena

Abstract

We investigate the dynamics of a gas of non-interacting particle-like soliton waves, demonstrating that phase transitions originate from their collective behavior. This is predicted by solving exactly the nonlinear equations and by employing methods of the statistical mechanics of chaos. In particular, we show that a suitable free energy undergoes a metamorphosis as the input excitation is increased, thereby developing a first order phase transition whose measurable manifestation is the formation of shock waves. This demonstrates that even the simplest phase-space dynamics, involving independent (uncoupled) degrees of freedom, can sustain critical phenomena.