Dynamical fluctuation theory in a nutshell

A dynamical fluctuation is an atypical value of a time-integrated observable such as entropy production, particle current, or number of state transitions in a stochastic system. A comprehensive theory exists for how to characterize the likelihood of a dynamical fluctuation, and to determine the ensemble of system trajectories which realize it, given that the observation times involved are large. In this talk I will explain the basic elements of this theory in the context of Markov jump processes. While somewhat technical, most of the developments can be made physically intuitive by exploiting the clear analogy to ensemble theory in equilibrium physics, with distributions over microstates generalized to distribution of dynamical trajectories, and the large N-limit replaced by the large t-limit. In the following session we apply these tools to an analytically solvable model.