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

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.

8 pages

References in corpus (5)

• Optimal finite-time processes in stochastic thermodynamics
• The geometry of thermodynamic control
• Fluctuation Relations for Diffusion Processes
• Thermodynamic transformations of nonequilibrium states
• The Monge-Ampère-Kantorovich approach to reconstruction in cosmology

Cited by in corpus (10)

• Dynamic Riemannian Geometry of the Ising Model
• Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics
• Summing over trajectories of stochastic dynamics with multiplicative noise
• E. Schrödinger's 1931 paper "On the Reversal of the Laws of Nature" ["Über die Umkehrung der Naturgesetze",Sitzungsberichte der preussischen Akademie der Wissenschaften, physikalische mathematische Klasse, 8 N9 144-153]
• Optimality of non-conservative driving for finite-time processes with discrete states
• Generally covariant state-dependent diffusion
• On extremals of the entropy production by "Langevin-Kramers" dynamics
• An application of Pontryagin's principle to Brownian particle engineered equilibration
• Optimal Control of Underdamped Systems: An Analytic Approach
• Optimal protocols and the Jarzynski equality