These days I’ll try to (irregularly) live-blog from the workshop Statistical Mechanics and Computation of Large Deviation Rate Functions at ENS, Lyon. Apparently talks will be recorded and put online. The emphasis is supposed to be on techniques for computation and even on experiment, rather than theory (so my talk will fall a bit off…).
Eric Vanden-Eijnden – Pathways and Flows in Metastable Marko Chains. An introductory talk, mainly qualitative. The main message: keeping into account entropic effects, beyind energetic, for understanding rare exents. He focused on detailed balanced systems. In particular, metastability: hopping between states separated by bottlenecks that are not energetic, but rather entropic, “dynamical”. A systems is trapped into a state until a large deviation (a rare event) pushes it outside. An illuminating example of a large deviations of entropic origin: a Brownian particle in a maze is guided by no energy, but it takes a rare event to have it walk all the way through the maze. Methods to compute rare events include: spectral methods, if there is a time-scale separation between a higher and a lower bunch of eigenvalues (and if the corresponding eigenvectors are localized), then one can approximate the transitions by a Markov jump process (here the interesting concept of “eigencurrent” was mentioned but not explained). However, computing eigenvalues might be difficult. Hence one might resort to Transition Path Theory. Many examples follow, but it’s hard to see the picture.
Todd Gingrich – Efficient Path Sampling of Ising Dynamics for Identifying Low-Dissipation PRotocols. Joint work with Crooks, Rostkoff, Geissler. The problem is to sample nonequilibrium protocols that drive processes. Examples from Ising model with Glauber dynamics: In this case a protocol would be a transition from positive to negative magnetic fields in a finite amount of time. One can then consider the probability of a trajectory given a protocol. The idea is to exploit large deviations theory to understand low-dissipation protocols. From a chemist’s perspective, the protocol space is high-dimensional (not just stiffness and height as in Schmiedl & Seifert, Zulkowski et al., etc.). Not all parts of the protocol need to be tightly controlled. The idea is to resort to perturbations, looking how modifying the protocol improves on worsens dissipation. Unfortunately this is very expensive computationally, as one spends a lot of time computing averages rather than sampling the protocol. He then resorts to an assumption of linear regime, basically a Gaussian approximation for the dissipation, and now one can easily calculate the marginal for the protocol. A technical problem that emerges (did’nt understand why exactly) is to sample correlated trajectories that do not differ too much, and the lesson to be learned is that one has to play some dirty tricks directly with the noise rather than biasing the MonteCarlo update rules.