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Statistical mechanics of holonomic systems as a Brownian motion on smooth manifolds
Author(s) -
Manca Fabio,
Déjardin PierreMichel,
Giordano Stefano
Publication year - 2016
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.201500221
Subject(s) - brownian motion , statistical mechanics , classical mechanics , physics , manifold (fluid mechanics) , covariant transformation , context (archaeology) , langevin equation , smoluchowski coagulation equation , holonomic constraints , brownian dynamics , equations of motion , statistical physics , holonomic , langevin dynamics , mathematical physics , quantum mechanics , mechanical engineering , paleontology , engineering , biology
The statistical mechanics of arbitrary holonomic scleronomous systems subjected to arbitrary external forces is described by specializing the Lagrange and Hamilton equations of motion to those of the Brownian motion on a manifold. In this context, the Klein‐Kramers and Smoluchowski equations are derived in covariant form, and it is demonstrated that these equations have equilibrium solutions corresponding to the Gibbs distribution, in agreement with standard thermodynamics. At last, the Langevin dynamics corresponding to the Smoluchowski limit is found to exactly correspond to the Brownian motion on a smooth manifold. These results find significant applications in the study of several statistical properties of constrained molecular assemblies (e.g. polymers) of interest in chemistry, physics and biology.