Detailed Balance and Free-energy
by R. F. Streater,
pp 56-65, "Quantum Information Theory and Open Systems",
(eds. H. Nagaoka and M. Ohya), Surikaisekikenkyusho-Kokyuroka, No 980,
(Kyoto), 1997.
ABSTRACT
We formulate the notion of detailed balance at a given beta for
a discrete Markov chain, and show that it
implies that one time-step
in the chain is a contraction in the norm ||bullet||{_beta}$; this is
defined on the set of states as the dual to the norm on the random
variables given by the classical KMS state. It is shown that if the initial
state is close to equilibrium in a suitable sense, then an irreducible
chain converges to equilibrium in the sense of the dual norm.
Go to my HOME PAGE
for links to other works on quantum field theory and statistical
mechanics.
© by Ray Streater, 13/6/00