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Identities for nonlinear memory kernels
Juliana Caspers1, Matthias Krüger1
1Georg-August-Universität Göttingen, Institute for Theoretical Physics, 37073 Göttingen, Germany.
Physical Review. E
|September 16, 2025
Summary
Researchers derived new identities for nonlinear memory kernels in systems far from equilibrium. These findings extend the fluctuation-dissipation theorem and offer a new way to analyze nonequilibrium systems using Volterra series.
Area of Science:
- Statistical mechanics
- Nonlinear dynamics
- Theoretical physics
Background:
- Systems far from equilibrium are challenging to model.
- Nonlinear Volterra series offer a formal description for time-dependent perturbations.
- Understanding memory kernels is crucial for characterizing system dynamics.
Purpose of the Study:
- Derive novel identities for nonlinear memory kernels.
- Extend the fluctuation-dissipation theorem to nonlinear regimes.
- Establish a framework for analyzing nonequilibrium systems.
Main Methods:
- Formal derivation of identities for nonlinear memory kernels.
- Utilizing the principle of local detailed balance.
- Testing derived identities via simulations of driven Brownian particles.
Main Results:
- Identities for nonlinear memory kernels were successfully derived.
- The fluctuation-dissipation theorem was identified as the lowest-order identity.
- A series relation for nonequilibrium cumulants was established.
Conclusions:
- The derived identities provide a powerful tool for studying nonequilibrium systems.
- These findings offer new insights into the behavior of driven systems.
- The framework connects nonlinear response theory with statistical mechanics principles.
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