Fluctuations out of equilibrium

Area of Science:

• Statistical physics
• Non-equilibrium thermodynamics
• Complex systems

Background:

• The fluctuation-dissipation theorem (FDT) traditionally relates system fluctuations to dissipation.
• Understanding fluctuation-dissipation relations in systems with time-varying parameters is crucial for non-equilibrium statistical mechanics.

Purpose of the Study:

• To generalize the fluctuation-dissipation theorem for systems with slowly varying parameters.
• To investigate the role of dispersive contributions alongside dissipative ones in determining fluctuation spectral functions.

Main Methods:

• Application of the Langevin method.
• Utilizing the method of moments.
• Employing a multiscale technique.

Main Results:

• Demonstrated that both dissipative and dispersive contributions are essential for determining spectral functions of fluctuations.
• Identified a novel non-Joule dispersive contribution characterized by a non-local effect.
• Showed this non-local effect arises from an additional phase shift induced by parametric control.

Conclusions:

• The generalized FDT provides a more comprehensive description of fluctuations in arbitrary statistical systems, especially under parametric control.
• Dispersive effects, previously overlooked in some contexts, play a significant role in the dynamics of fluctuations.
• The findings have implications for understanding complex systems operating out of equilibrium.