Nonlinear response relations and fluctuation-response inequalities for nonequilibrium stochastic systems.

Area of Science:

• Physics, chemistry, and biology
• Complex systems far from equilibrium
• Stochastic thermodynamics

Background:

• Predicting system responses to perturbations far from equilibrium is a significant scientific challenge.
• Existing theories often struggle to unify linear and nonlinear response regimes.
• Understanding these dynamics is crucial for fields ranging from molecular biology to materials science.

Purpose of the Study:

• To develop a unified response framework for stochastic Markov dynamics.
• To integrate both linear and nonlinear perturbations within a single theoretical approach.
• To provide new insights into the behavior of systems far from thermodynamic equilibrium.

Main Methods:

• Developed a formalism to express nonlinear responses using the covariance between an observable and a nonlinear conjugate variable.
• Utilized the complete Bell polynomial form for the nonlinear conjugate variable.
• Derived fluctuation-response inequalities for nonlinear responses.

Main Results:

• Established a unified framework applicable to both linear and nonlinear perturbations in stochastic systems.
• Quantified nonlinear responses through a connection to stochastic entropy production.
• Unraveled trade-off relations between nonlinear response and system fluctuations far from equilibrium.

Conclusions:

• The proposed theory unifies and extends existing nonequilibrium linear response theories.
• The framework offers principled design rules for creating sensitive and adaptive synthetic and biological networks.
• Validated through numerical simulations of a symmetric exclusion process.