A dynamical system theoretical approach to equilibrium statistical mechanics (Q2752319)

In previous papers, the author has proposed a generalization of the conventional model of dynamical systems (based on differential equations) that introduces explicitly the rule of time evolution and measurement theory. To this end, he stated a set of axioms involving such concepts as pure state and mixed state, exactly like in quantum mechanics, via \(C^*\)-algebras. The measurement theory combines classical measurement theory and quantum measurement theory. After a short section delivering some background on this algebraic modelling of dynamical system and some comments about it, it is shown that it provides new points of view on equilibrium in statistical mechanics. This is an abstract mathematical paper, something like the theory of categories.