2021
DOI: 10.48550/arxiv.2109.01990
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A simple hypocoercivity analysis for the effective Mori-Zwanzig equation

Abstract: We provide a simple hypocoercivity analysis for the effective Mori-Zwanzig equation governing the time evolution of noise-averaged observables in a stochastic dynamical system. Under the hypocoercivity framework mainly developed by Dolbeault, Mouhot and Schmeiser and further extended by Grothaus and Stilgenbauer, we prove that under the same conditions which lead to the geometric ergodicity of the Markov semigroup e tK , the Mori-Zwanzig orthogonal semigroup e tQKQ is also geometrically ergodic, provided that … Show more

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“…Another systematic route to reduce the dimensionality of a system is given by the projection operator formalism [8][9][10]43]. In the following, we will focus on the MZ formalism, which was originally developed for Hamiltonian dynamics, but has been shown to also be applicable to stochastic systems [22][23][24][44][45][46]. In the next subsection, we will shortly recap the important properties of the MZ formalism along the lines of reference [24], and then explicitly evaluate the formal expressions for the specific SDE discussed in this work.…”
Section: Projection Operator Formalismmentioning
confidence: 99%
“…Another systematic route to reduce the dimensionality of a system is given by the projection operator formalism [8][9][10]43]. In the following, we will focus on the MZ formalism, which was originally developed for Hamiltonian dynamics, but has been shown to also be applicable to stochastic systems [22][23][24][44][45][46]. In the next subsection, we will shortly recap the important properties of the MZ formalism along the lines of reference [24], and then explicitly evaluate the formal expressions for the specific SDE discussed in this work.…”
Section: Projection Operator Formalismmentioning
confidence: 99%