Large deviations of work distributions for RNA secondary structures and for other distributions and models

Alexander Hartmann (U Oldenburg)

Oct 06. 2022, 10:00 — 11:00

A "black-box" approach to study large-deviation properties of distributions of quantities of interest is presented. It is based on performing Markov chain Monte Carlo simulations in the space of random number vectors plus, as usual, applying suitable biases. These random number are used to drive, e.g., non-equilibrium processes, resulting in a scalar value, which can be used to implement bias of the Markov chain in order to access the distribution of interest, which is obtained finally after suitable rescaling. Here, we consider as example the distribution of work of driven processes, in particular the Ising model driven by an extarnal field and RNA secondary structures driven by external mechanical forces. The distribution P(W) of work has been obtained in this way over more than hundred decades in probability. This allowed us to verify Crooks theorem and the Jarzynski relation even for rather large systems, where one has to access the tails of the distributions. Also we measured how close the non-equilibrium processes are to the equilibrium ones, depending on the work value W. Other recent applications of this and related approaches allowed us to study the distributions, up to more than 1000 decades in probability, of heights in the Kardar-Parisi-Zhang equation, of convex hulls of various types of random walks, of the dynamics of disease spreading in the SIR model, of the traffic flow in the Nagel-Schreckenberg model, of displacements for fractional Brownian motion, of the  stability of electrical grids and other transport networks, of the length of longest increasing subsequences, of the time to the first common ancestor in population model, and many others.

Further Information
Venue:
ESI Schrödinger and Boltzmann Lecture Hall
Associated Event:
Large Deviations, Extremes and Anomalous Transport in Non-equilibrium Systems (Thematic Programme)
Organizer(s):
Christoph Dellago (U of Vienna)
Satya Majumdar (U Paris Sud, Orsay)
David Mukamel (Weizmann Institute, Rehovot)
Harald Posch (U of Vienna)
Gregory Schehr (U Paris Sud, Orsay)