Weak Galilean invariance as a selection principle for coarse-grained diffusive models

Proceedings of the National Academy of Sciences of the United States of America
Andrea CairoliAdrian Baule

Abstract

How does the mathematical description of a system change in different reference frames? Galilei first addressed this fundamental question by formulating the famous principle of Galilean invariance. It prescribes that the equations of motion of closed systems remain the same in different inertial frames related by Galilean transformations, thus imposing strong constraints on the dynamical rules. However, real world systems are often described by coarse-grained models integrating complex internal and external interactions indistinguishably as friction and stochastic forces. Since Galilean invariance is then violated, there is seemingly no alternative principle to assess a priori the physical consistency of a given stochastic model in different inertial frames. Here, starting from the Kac-Zwanzig Hamiltonian model generating Brownian motion, we show how Galilean invariance is broken during the coarse-graining procedure when deriving stochastic equations. Our analysis leads to a set of rules characterizing systems in different inertial frames that have to be satisfied by general stochastic models, which we call "weak Galilean invariance." Several well-known stochastic processes are invariant in these terms, except the continuous-ti...Continue Reading

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Citations

Sep 11, 2019·Physical Review. E·F Le VotE Abad
May 22, 2019·Physical Review. E·Yao ChenWeihua Deng
Feb 20, 2021·Physical Review. E·Yao Chen, Weihua Deng

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