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arXiv · 1210.1133

On the use of stochastic differential geometry for non-equilibrium thermodynamics modeling and control

Paolo Muratore-Ginanneschi
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Abstract

We discuss the relevance of geometric concepts in the theory of stochastic differential equations for applications to the theory of non-equilibrium thermodynamics of small systems. In particular, we show how the Eells-Elworthy-Malliavin covariant construction of the Wiener process on a Riemann manifold provides a physically transparent formulation of optimal control problems of finite-time thermodynamic transitions. Based on this formulation, we turn to an evaluative discussion of recent results on optimal thermodynamic control and their interpretation.

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Paolo Muratore-Ginanneschi. 2012-10-03. On the use of stochastic differential geometry for non-equilibrium thermodynamics modeling and control. https://doi.org/10.1088/1751-8113%2F46%2F27%2F275002

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