# On the Relation between Gradient Flows and the Large-Deviation Principle, with Applications to Markov Chains and Diffusion

@article{Mielke2013OnTR, title={On the Relation between Gradient Flows and the Large-Deviation Principle, with Applications to Markov Chains and Diffusion}, author={Alexander Mielke and Mark A. Peletier and D. R. Michiel Renger}, journal={Potential Analysis}, year={2013}, volume={41}, pages={1293-1327} }

Motivated by the occurrence in rate functions of time-dependent large-deviation principles, we study a class of non-negative functions ℒ that induce a flow, given by ℒ(ρt,ρ̇t)=0$\mathcal{L} (\rho _{t},\dot \rho _{t})=0$. We derive necessary and sufficient conditions for the unique existence of a generalized gradient structure for the induced flow, as well as explicit formulas for the corresponding driving entropy and dissipation functional. In particular, we show how these conditions can be…

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