# Thermodynamic conditions governing the optical temperature and chemical potential in nonlinear highly multimoded photonic systems

## TL;DR

This paper demonstrates that complex weakly nonlinear multimode photonic systems can attain thermodynamic equilibrium with well-defined temperature and chemical potential, depending on system spectrum, input power, and Hamiltonian invariants.

## Contribution

It derives explicit conditions for positive or negative temperatures in multimode photonic systems based on their linear spectrum and input parameters.

## Key findings

- Thermodynamic equilibrium characterized by unique temperature and chemical potential.
- Conditions for positive or negative temperatures derived explicitly.
- Examples illustrating the theoretical results across different scenarios.

## Abstract

We show that, in general, any complex weakly nonlinear highly multimode system can reach thermodynamic equilibrium that is characterized by a unique temperature and chemical potential. The conditions leading to either positive or negative temperatures are explicitly obtained in terms of the linear spectrum of the system, the input power, and the corresponding Hamiltonian invariant. Pertinent examples illustrating these results are provided in various scenarios.

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Source: https://tomesphere.com/paper/1908.01708