Thermodynamic uncertainty relations in the presence of non-linear friction and memory

A new Thermodynamic Uncertainty Relation (TUR) is derived for systems described by linearly coupled Langevin equations in the presence of non-linear frictional forces. In our scheme, the main variable represents the velocity of a particle, while the other coupled variables describe memory effects wh...

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Bibliographic Details
Published in:arXiv.org 2023-12
Main Authors: Plati, A, Puglisi, A, Sarracino, A
Format: Article
Language:English
Subjects:
Diffusion coefficient
Lower bounds
Thermal baths
Thermodynamics
Uncertainty
Online Access:Get full text
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Summary:A new Thermodynamic Uncertainty Relation (TUR) is derived for systems described by linearly coupled Langevin equations in the presence of non-linear frictional forces. In our scheme, the main variable represents the velocity of a particle, while the other coupled variables describe memory effects which may arise from strongly correlated degrees of freedom with several time-scales and, in general, are associated with thermal baths at different temperatures. The new TUR gives a lower bound for the mean-squared displacement of the position of the particle, including its asymptotic diffusion coefficient. This bound, in several examples worked out here, appears to be a good analytical estimate of the real diffusion coefficient. The new TUR can be also applied in the absence of any external force (with or without thermal equilibrium between the baths), a case which usually goes beyond the scope of original TURs. We show applications to non-linear frictional models with memory, such as the Coulomb and the Prantdtl-Tomlinson models, usually representative of friction at the nano-scale and within atomic-force microscopy experiments.
ISSN:2331-8422
DOI:10.48550/arxiv.2312.15243