Abstract
Motivated from the chemical potential theory, we study quantum statistical thermodynamics in AF C*-systems generalizing usual one-dimensional quantum lattice systems. Our systems are C*-algebras [Formula: see text] which have a localization [Formula: see text] of finite-dimensional subalgebras indexed by finite intervals of Z and an automorphism γ acting as a right shift on the localization. Model examples are supplied from derived towers (string algebras) for type II1 factor-subfactor pairs. Given a (γ-invariant) interaction and a specific tracial state, we formulate the Gibbs conditions and the variational principle for (γ-invariant) states on [Formula: see text], and investigate the relationship among these conditions and the KMS condition for the time evolution generated by the interaction. Special attention is paid to C*-systems of gauge invariance (typical model in the chemical potential theory) and to C*-systems considered as quantum random walks on discrete groups. The CNT-dynamical entropy for the shift automorphism γ is also discussed.
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