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.

%B PHYSICAL REVIEW X %V 7 %R 10.1103/PhysRevX.7.031027 %0 Journal Article %J {PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES} %D 0 %T {Quantum reference frames and their applications to thermodynamics} %A Popescu, Sandu %A Belen Sainz, Ana %A Short, Anthony J. %A Winter, Andreas %X{We construct a quantum reference frame, which can be used to approximately implement arbitrary unitary transformations on a system in the presence of any number of extensive conserved quantities, by absorbing any back action provided by the conservation laws. Thus, the reference frame at the same time acts as a battery for the conserved quantities. Our construction features a physically intuitive, clear and implementation-friendly realization. Indeed, the reference system is composed of the same types of subsystems as the original system and is finite for any desired accuracy. In addition, the interaction with the reference frame can be broken down into two-body terms coupling the system to one of the reference frame subsystems at a time. We apply this construction to quantum thermodynamic set-ups with multiple, possibly non-commuting conserved quantities, which allows for the definition of explicit batteries in such cases. This article is part of a discussion meeting issue `Foundations of quantum mechanics and their impact on contemporary society'.}

%B {PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES} %V {376} %8 {JUL 13} %R {10.1098/rsta.2018.0111}