The University of Arizona

Small Mass Limit of Noisy Inertial Particle Dynamics: Homogenization and Instantaneous Equilibration

Small Mass Limit of Noisy Inertial Particle Dynamics: Homogenization and Instantaneous Equilibration

Series: Mathematical Physics and Probability Seminar
Location: Math 402
Presenter: Jeremiah Birrell, University of Arizona

I will discuss the dynamics of an inertial particle, coupled to forcing, dissipation, and noise, in the small mass limit. Specifically, I will show how the limit of the joint distribution of the position and (appropriately scaled) velocity degrees of freedom can be computed.  At a given time, and conditioned on the position of the particle, one finds that the distribution of the scaled velocity becomes Gaussian in the limit i.e. it maintains an instantaneous equilibrium distribution.   This result aids in the computation of the limits of important physical quantities, such as the expected value of the energy and entropy production, and provides additional insight into the form the homogenized limiting equation for the position degrees of freedom.

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