A Spectral Theorem for the Semigroup Generated by a Class of Infinitely Many Master Equations

In this article we investigate the spectral properties of infinitesimal generator an infinite system master equations arising in analysis approach to equilibrium statistical mechanics. The under consideration thus consists infinitely many first-order differential governing time evolution probabilities susceptible describing jumps between eigenstates a operator with discrete point spectrum. transition rates are chosen such way that so-called detailed balance conditions satisfied, so for large class initial given possesses global solution which converges exponentially rapidly toward independent probability Gibbs type. A particular feature and challenge problem is infinite-dimensional functional space where initial-value well posed, realized as non normal dissipative compact operator, whose spectrum therefore does not exhibit gap around zero eigenvalue.