PreprintCC BY 4.0arXiv
Thermodynamic Bounds from Otto--Villani Functional Inequalities
Abstract
The dissipation in the relaxation of an ensemble of conservative stochastic systems towards the equilibrium steady state is quantified by the free energy difference. Functional inequalities within the framework of [F. Otto and C. Villani, J. Funct. Anal. 173, 361 (2000)] are here revisited which connect the free energy dynamics and optimal transport, offering a geometric perspective on the instantaneous speed of relaxation in the presence of potential barriers. These are illustrated with numerical relaxation experiments on Landau-Ginzburg potentials. The same inequalities hold for relaxation toward nonequilibrium steady states once the potential is replaced by the pseudo-potential defined by the stationary density.
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BibTeX
@misc{auconi2026thermodynamic,
title = {{Thermodynamic Bounds from Otto--Villani Functional Inequalities}},
author = {Andrea Auconi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.14329},
eprint = {2606.14329},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.14329},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Thermodynamic Bounds from Otto--Villani Functional Inequalities
AU - Andrea Auconi
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2606.14329
UR - https://arxiv.org/abs/2606.14329
AB - The dissipation in the relaxation of an ensemble of conservative stochastic systems towards the equilibrium steady state is quantified by the free energy difference. Functional inequalities within the framework of [F. Otto and C. Villani, J. Funct. Anal. 173, 361 (2000)] are here revisited which connect the free energy dynamics and optimal transport, offering a geometric perspective on the instantaneous speed of relaxation in the presence of potential barriers. These are illustrated with numerical relaxation experiments on Landau-Ginzburg potentials. The same inequalities hold for relaxation toward nonequilibrium steady states once the potential is replaced by the pseudo-potential defined by the stationary density.
ER -