Thermodynamic constraints on the nonequilibrium response of one-dimensional diffusions

Area of Science:

• Statistical Mechanics
• Non-equilibrium Physics
• Dynamical Systems

Background:

• Non-equilibrium steady states (NESS) are crucial for understanding systems driven by continuous energy input.
• Analyzing the response of NESS to perturbations is challenging due to their inherent complexity.
• One-dimensional diffusion on a circle provides a tractable model for studying NESS properties.

Purpose of the Study:

• To develop a general framework for analyzing the static response of one-dimensional diffusion models on a circle to arbitrary perturbations.
• To simplify the analysis of perturbation responses by decomposing them into fundamental classes.
• To derive quantitative formulas for characterizing the response strength, valid even far from equilibrium.

Main Methods:

• Decomposition of arbitrary perturbations into three fundamental classes.
• Derivation of analytical formulas for the static response to each perturbation class.
• Analysis of the response in terms of the strength of the non-equilibrium driving force.

Main Results:

• Demonstration that any perturbation can be represented as a combination of three specific classes.
• Derivation of simple, quantitative formulas for the system's static response.
• The derived formulas are valid for arbitrary strengths of non-equilibrium driving, extending beyond near-equilibrium approximations.

Conclusions:

• The developed method offers a powerful and simplified approach to understanding the response of NESS in one-dimensional diffusion models.
• The quantitative formulas provide valuable insights into system dynamics and stability under non-equilibrium conditions.
• This work lays the groundwork for analyzing more complex systems and perturbations in non-equilibrium statistical mechanics.