We address the problem of understanding, from first principles, the conditions under which a quantum system equilibrates rapidly with respect to a concrete observable. On the one hand, previously known general upper bounds on the time scales of equilibration were unrealistically long, with times scaling linearly with the dimension of the Hilbert space. These bounds proved to be tight since particular constructions of observables scaling in this way were found. On the other hand, the computed equilibration time scales for certain classes of typical measurements, or under the evolution of typical Hamiltonians, are unrealistically short. However, most physically relevant situations fall outside these two classes. In this paper, we provide a new upper bound on the equilibration time scales which, under some physically reasonable conditions, give much more realistic results than previously known. In particular, we apply this result to the paradigmatic case of a system interacting with a thermal bath, where we obtain an upper bound for the equilibration time scale independent of the size of the bath. In this way, we find general conditions that single out observables with realistic equilibration times within a physically relevant setup.

1 aGarcia-Pintos, Luis, Pedro1 aLinden, Noah1 aMalabarba, Artur, S. L.1 aShort, Anthony, J.1 aWinter, Andreas uhttps://grupsderecerca.uab.cat/giq/node/84400485nas a2200157 4500008003900000022001400039245004900053210004500102260001200147300001400159490000800173100001700181700001900198700002000217856009000237 2013 d a0018-944800aThe structure of Renyi entropic inequalities0 astructure of Renyi entropic inequalities c10/2013 a20120737 0 v4691 aLinden, Noah1 aMosonyi, Milan1 aWinter, Andreas uhttps://grupsderecerca.uab.cat/giq/publications/structure-renyi-entropic-inequalities