Multidimensional characterization of stochastic dynamical systems based on multiple perturbations and measurements

Area of Science:

• Physics
• Chemistry
• Biophysics

Background:

• Stochastic dynamical systems are prevalent in various scientific fields.
• Understanding their dynamics under perturbations is crucial.
• Existing methods may not fully capture complex nonlinear responses.

Purpose of the Study:

• To present a generalized nonlinear response theory for stochastic dynamical systems.
• To introduce generalized response functions (GRFs) as novel multidimensional measures.
• To provide a framework for analyzing system dynamics under various perturbations.

Main Methods:

• Derivation of closed expressions for GRFs in stochastic systems.
• Comparison of theoretical GRFs with numerical non-equilibrium simulations.
• Consideration of diverse perturbations: temperature (impulsive, periodic) and coordinate (impulsive).

Main Results:

• Generalized response functions (GRFs) are defined as multidimensional measures of stochastic dynamics.
• Theoretical expressions for GRFs are derived.
• GRFs are validated through comparison with numerical simulations.

Conclusions:

• The presented theory and GRFs offer a powerful tool for characterizing stochastic dynamics.
• This approach is applicable to a wide range of systems, including single-molecule dynamics and chemical kinetics.
• The framework facilitates the study of complex system responses to perturbations.