Entanglement and the Foundations of Statistical Mechanics
(based on work with S Popescu and T Short, Nature Phys. 2(11):754-758, 2006
and with N Linden, S Popescu and T Short, arXiv:0812.2385)
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. In the second part of our work,
we 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 equilibrium state has the
character of a canonical state.