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Exact Response Theory for Time-Dependent and Stochastic Perturbations
Leonardo Iannella1, Lamberto Rondoni2,3
1Dipartimento di Fisica, Università di Torino, Via Pietro Giuria 1, 10125 Torino, Italy.
Entropy (Basel, Switzerland)
|January 26, 2024
Summary
This study extends exact response theory to include time-dependent stochastic perturbations. The enhanced theory, using the Karhunen-Loève theorem, offers new ways to analyze complex dynamical systems.
Area of Science:
- Non-equilibrium statistical mechanics
- Theoretical physics
- Computational chemistry
Background:
- Non-equilibrium molecular dynamics (NEMD) provides exact response theory.
- Transient time correlation function (TTCF) is a key element, quantifying dissipated power.
- Existing theory handles time-independent and dependent perturbations in deterministic systems.
Purpose of the Study:
- To incorporate time-dependent stochastic perturbations into exact response theory.
- To extend the applicability of TTCF to systems with random influences.
- To provide a framework for analyzing systems not amenable to linear response theory.
Main Methods:
- Application of the Karhunen-Loève theorem to stochastic processes.
- Development of three distinct averaging schemes for stochastic perturbations.
- Analysis of dynamical systems with both initial condition and stochastic coefficient variations.
Main Results:
- The generalized theory accommodates time-dependent stochastic perturbations.
- Three novel investigation approaches are presented for stochastic processes.
- The dissipation function remains central in the extended theoretical framework.
Conclusions:
- The enhanced exact response theory is applicable to a broader range of dynamical systems.
- The inclusion of stochasticity provides deeper insights into system behavior.
- The theory's utility is demonstrated through illustrative examples.
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