The non-equilibrium dynamics of a strongly correlated quantum system is one of the most fascinating problems in physics, with open questions regarding when and how thermalization occurs and what the equilibrium state is like. Unusual phenomena are observed when the system exhibits conserved quantities that constrain its evolution in phase space, invalidating the predictions of standard quantum thermodynamics. We have derived generalized versions of the quantum Jarzynski equality and the Tasaki-Crooks relation for these systems, and provide numerical simulations showing that these novel quantum fluctuation relations can be tested with available technology in trapped ion setups. Our results pave the way for a deeper understanding of the role of conserved quantities in non-equilibrium processes.
 J. Mur-Petit, A. Relaño, R. A. Molina, D. Jacksch, Nature Communications 9, 2006 (2018)
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