D. Ruelle
Natural nonequilibrium states in quantum statistical mechanics.
(44K, Plain TeX with one ps figure)
ABSTRACT. A quantum spin system is discussed, where a heat flow between infinite
reservoirs takes place in a finite region. A time dependent force may
also be acting. Our analysis is based on a simple technical
assumption concerning the time evolution of infinite quantum spin
systems. This assumption, physically natural but currently proved for
few specific systems only, says that quantum information diffuses in
space-time in such a way that the time integral of the commutator of
local observables converges:
$\int_{-\infty}^0dt\,||[B,\alpha^tA]||<\infty$.
In this setup one can define a natural nonequilibrium state. In the
time independent case, this nonequilibrium state retains some of the
analyticity which characterizes KMS equilibrium states. A linear
response formula is also obtained which remains true far from
equilibrium. The formalism presented here does not cover situations
where (for time independent forces) the time translation invariance
and uniqueness of the natural nonequilibrium state are broken.