I will explain how, in systems with quantum Markovian dynamics, it is possible to define a "statistical mechanics of trajectories", that is, a framework for studying ensembles of trajectories in a manner analogous to ensembles of configurations in equilibrium statistical mechanics. This provides the natural platform to describe and characterise complex non-equilibrium behaviour borrowing from concepts from equilibrium thermodynamics. I will illustrate these ideas with simple examples of open quantum systems displaying intermittency and metastability, and show how such dynamics can be related to the existence of competing (dynamical) phases and transitions between them. Time permitting I will discuss the some or all of the following: (i) the connection to matrix product states, (ii) applications to state smoothing and prediction/retrodiction, (iii) how to engineer systems that display as their typical dynamics the rare atypical behaviour of another system of interest, (iv) a "level 2.5" of large deviations (i.e., large deviation statistics of all possible dynamical observables) for open quantum systems.
By Florian Marquardt
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By Yassine Hamoudi
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By Nana Liu
