Thermodynamic bounds for diffusion in nonequilibrium systems with multiple timescales

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Complex Systems

Background:

• Understanding the behavior of systems driven out of equilibrium is crucial in statistical mechanics.
• Gaussian processes with memory exhibit complex dynamics, often displaying anomalous diffusion.
• Existing thermodynamic uncertainty relations have limitations in finite time and for systems with memory.

Purpose of the Study:

• To derive a novel thermodynamic uncertainty relation for Gaussian processes with memory.
• To provide a tighter bound on the mean squared displacement compared to previous results.
• To develop a tool for distinguishing equilibrium from nonequilibrium behavior in complex systems.

Main Methods:

• Derivation of a thermodynamic uncertainty relation using principles of stochastic thermodynamics.
• Analysis of Gaussian processes incorporating memory effects.
• Application and validation using experimental and numerical data from vibrofluidized granular media.

Main Results:

• A new, tighter thermodynamic uncertainty relation for the mean squared displacement of Gaussian processes with memory.
• The derived bound is applicable at finite times, overcoming previous limitations.
• Demonstrated the relation's ability to differentiate between equilibrium and nonequilibrium regimes in granular media.

Conclusions:

• The new thermodynamic uncertainty relation offers a more precise tool for analyzing systems with memory.
• This work provides a valuable method for inferring the thermodynamic state of complex systems.
• The findings have implications for understanding anomalous diffusion and nonequilibrium statistical mechanics.