Theoretical Physics Colloquium
Conditioned stochastic processes
by Dr. Tridib Sadhu (TIFR)
Tuesday, June 4, 2019 from to (Asia/Kolkata)
An interesting question in statistical physics is what evolution a system undergoes when it is conditioned to satisfy a certain constraint. For example, a Brownian motion conditioned to end at a certain point, a Langevin process conditioned to perform a certain amount of work in a time interval, or a transport model conditioned to produce a fixed amount of flux. The last two are examples of conditioning on a time-integrated quantity or empirical observable. I shall discuss, how one can describe conditioned dynamics and fluctuations in such constrained ensembles. The analysis will be presented in a pedagogical style, starting from a Markov chain, to Langevin processes, and then to a fluctuating hydrodynamics description for systems with many degrees of freedom. In addressing these questions, I shall also discuss how the concepts of thermodynamic ensembles and their equivalence can be extended outside equilibrium, and their relation to dynamical phase transitions.