2017-05-17
10:15 at HCP F 43.4

A generalisation of the fluctuation-dissipation relation of the second kind through large-deviation theory

Alberto Montefusco

Polymer Physics, Department of Materials, ETH Zurich

Properly formulating stochastic models is a very important task of a thermodynamicist, for both theoretical developments and purposes of simulation. The present work deals with the mutual structural properties of a class of stochastic systems and their corresponding deterministic limit. Fluctuation-dissipation relations are very general properties of many systems in statistical mechanics. A Fluctuation-dissipation relation of the second kind (FDR2) establishes a relationship between the frictional properties of a system and the stochastic noise on a system, both resulting from the interaction with an environment. A FDR2 is generally formulated for Langevin dynamics, where it provides a one-to-one relationship between the structures of the drift term and the diffusion matrix. We call this formulation a classical FDR2. The aim of this talk [work] is to lift a FDR2 to more general processes in the following way. Firstly, we see a classical FDR2 from the perspectives of large-deviation theory and gradient flows: the former concerns the properties of the stochastic system and the latter represents the structure of the corresponding deterministic limit. Next, we realise that this viewpoint provides a straightforward lift to any general sequence of reversible Markov processes satisfying a large-deviation principle. Finally, we provide an abstract formulation of a FDR2, which appears as a relationship between the large-deviation properties of a stochastic system and the (generalised) gradient structure of the corresponding deterministic limit. We provide an explicit example in the context of chemical reactions in a well-stirred volume, which is the typical benchmark for extension of nonequilibrium thermodynamic theories to the nonlinear regime.