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.