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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

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Minimum-dissipation principle for synchronized stochastic oscillators far from equilibrium.

Jan Meibohm^1,2, Massimiliano Esposito³

¹<a href="https://ror.org/03v4gjf40">Technische Universität Berlin</a>, Straße des 17. Juni 135, 10623 Berlin, Germany.

Physical Review. E

|November 20, 2024

Summary

This summary is machine-generated.

We found a stability-dissipation relation for driven Potts models, linking entropy production to stability near a synchronization transition. This implies a minimum-dissipation principle for nonequilibrium systems.

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Area of Science:

Statistical Mechanics
Complex Systems
Non-equilibrium Physics

Background:

Potts models are used to study phase transitions.
Driven systems far from equilibrium exhibit complex dynamics.
Synchronization transitions are observed in various physical systems.

Purpose of the Study:

To establish a linear stability-dissipation relation (SDR) for q-state Potts models.
To investigate the connection between entropy production and stability near a synchronization transition.
To explore the implications of the SDR for minimum-dissipation principles in non-equilibrium systems.

Main Methods:

Theoretical analysis of q-state Potts models driven by nonconservative forces.
Investigation of the system's behavior near a critical coupling strength.
Derivation of the stability-dissipation relation and its connection to phase-space contraction.

Main Results:

A linear stability-dissipation relation (SDR) is proven for driven Potts models.
The SDR connects entropy production rate and phase-space contraction rate near a synchronization transition.
For large finite systems, the SDR implies a minimum-dissipation principle for stable non-equilibrium states.

Conclusions:

The stability-dissipation relation provides a fundamental link between stability and dissipation in driven systems.
The minimum-dissipation principle holds generally for driven Potts models, irrespective of the specific stochastic dynamics or the value of q.
This work offers insights into the behavior of complex systems operating far from thermodynamic equilibrium.