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Exact Response Theory for Time-Dependent and Stochastic Perturbations
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: Received: 17 November 2023 / Approved: 20 November 2023 / Online: 20 November 2023 (13:55:30 CET)
A peer-reviewed article of this Preprint also exists.
Iannella, L.; Rondoni, L. Exact Response Theory for Time-Dependent and Stochastic Perturbations. Entropy 2024, 26, 12. Iannella, L.; Rondoni, L. Exact Response Theory for Time-Dependent and Stochastic Perturbations. Entropy 2024, 26, 12.
Abstract
The exact, non perturbative, response theory developed within the field of nonequilibrium molecular
dynamics, also known as TTCF (Transient Time Correlation Function) applies to quite general dynamical systems. Its key element is called dissipation function, because it represents the power dissipated by external fields acting on the particle system of interest, whose coupling with the environment is
given by deterministic thermostats. This theory has been initially developed for time independent external perturbations, and then it has been extended to time dependent perturbations. It has also been applied to dynamical systems of different nature, and to oscillator models undergoing phase transitions, which cannot be treated withe.g. linear response theory. The present work includes time dependent stochastic perturbations, in the theory, using the Karhunen-Loeve theorem. This leads to three different investigations of a given process. One in which a single realization of the stochastic coefficients is fixed, and averages are taken only over the initial conditions, as in a deterministic process. In the second, the initial condition is fixed, and averages are taken with respect to the distribution of stochastic coefficients. In the last investigations, one averages over both initial conditions and stochastic coefficients. We conclude illustrating the applicability of the resulting exact response theory with simple examples.
Keywords
Nonequilibrium phenomena; Dissipation; Time Reversal Invariance; molecular dyanmics
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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