In recent work we uncovered intriguing connections between Otto’s characterization of diffusion as an entropic gradient flow on the one hand and large-deviation principles describing the microscopic picture (Brownian motion) on the other. In this paper, we sketch this connection, show how it generalizes to a wider class of systems and comment on consequences and implications. Specifically, we connect macroscopic gradient flows with large-deviation principles, and point out the potential of a bigger picture emerging: we indicate that, in some non-equilibrium situations, entropies and thermodynamic free energies can be derived via large-deviation principles. The approach advocated here is different from the established hydrodynamic limit passage but extends a link that is well known in the equilibrium situation.
|Journal||Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences|
|Early online date||18 Nov 2013|
|Publication status||Published - 28 Dec 2013|
Adams, S., Dirr, N., Peletier, M., & Zimmer, J. (2013). Large deviations and gradient flows. Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences, 371(2005), . https://doi.org/10.1098/rsta.2012.0341