Nonautomorphic dynamics in algebraic statistical mechanics

The scheme of the nonautomorphic dynamics in the algebraic statistical mechanics is proposed, which is based on the Heisenberg equations defined on algebras of microscopic observables. In contrast to the case of the automorphic dynamics these equations are not supposed to have the solutions in the algebra. The Liouville equations in the space of states are determined by the Heisenberg equations. General properties of the solutions of Liouville equations are investigated on certain sets of states, which we name quasi-equilibrium states. It is shown that the macroscopic causality principle is valid for the quasi-equilibrium states and in the representations determined by physically pure invariant states the dynamics is generated by the spatial group of automorphisms of the weak closure of the microscopic observable algebra.