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Abstract
We study the problem of Brownian motion in a multiscale potential. The potential is assumed to have N+1scales (i.e. N small scales and one macroscale) and to depend periodically on all the small scales. We show that for nonseparable potentials, i.e. potentials in which the microscales and the macroscale are fully coupled, the homogenized equation is an overdamped Langevin equation with multiplicative noise driven by the free energy, for which the detailed balance condition still holds. This means, in particular, that homogenized dynamics is reversible and that the coarsegrained Fokker–Planck equation is still a Wasserstein gradient flow with respect to the coarsegrained free energy. The calculation of the effective diffusion tensor requires the solution of a system of N coupled Poisson equations.
Original language  English 

Article number  82 
Number of pages  34 
Journal  Journal of Statistical Physics 
Volume  190 
Issue number  4 
DOIs  
Publication status  Published  31 Mar 2023 
Keywords
 Brownian dynamics
 Multiscale analysis
 Reiterated homogenization
 Reversible diffusions
 Free energy
 35B27
 60H30
 Article
 35Q82
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Dive into the research topics of 'Brownian Motion in an Nscale periodic Potential'. Together they form a unique fingerprint.Projects
 2 Finished

Rigorous coarsegraining of defects at positive temperature
Engineering & Physical Science Research Council
1/06/22 → 31/05/23
Project: Research Councils

Variational structures, convergence to equilibrium and multiscale analysis for nonMarkovian systems
Engineering & Physical Science Research Council
1/02/22 → 30/06/24
Project: Research Councils