Universidad Autònoma de Barcelona, Physics
We consider an alternative approach to the foundations of statistical mechanics, in which subjective randomness, ensemble-averaging or time-averaging are not required. Instead, the complete physical system (i.e. the subsystem of interest together with a sufficiently large environment) is in a quantum pure state subject to a global constraint, and thermalisation results from entanglement between system and environment. In the "kinematic" setting of statistical mechanics, we formulate and prove a "General Canonical Principle", which states that the system will be thermalised for almost all pure states of the universe, and provide rigorous quantitative bounds using Levy's Lemma. We then go on to consider a full dynamical model of equilibration in a setting of closed system Hamiltonian dynamics. We find conditions under which initial states equilibrate, and under which the equi-librium state has the character of a canonical state. [Based largely on work with S Popescu and T Short, Nature Phys. 2(11):754-758, 2006; and with N Linden, S Popescu and T Short, Phys. Rev. E79:061103, 2009].