Covariant currents and a thermodynamic uncertainty relation on curved manifolds

Harry J. D. Miller

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arXiv · 2407.15405

Covariant currents and a thermodynamic uncertainty relation on curved manifolds

Harry J. D. Miller

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Abstract

A framework for defining stochastic currents associated with diffusion processes on curved Riemannian manifolds is presented. This is achieved by introducing an overdamped Stratonovich-Langevin equation that remains fully covariant under non-linear transformations of state variables. The approach leads to a covariant extension of the thermodynamic uncertainty relation, describing a trade-off between the total entropy production rate and thermodynamic precision associated with short-time currents in curved spaces and arbitrary coordinate systems.

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Harry J. D. Miller. 2024-07-22. Covariant currents and a thermodynamic uncertainty relation on curved manifolds. https://arxiv.org/abs/2407.15405

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