A mathematical modeling of n-state systems

Abstract

In this paper, we assign a Riemannian manifold to $n$-state systems by using a canonical ensemble in equilibrium statistical mechanics. We consider discrete states with equal intervals, i.e., we assume equal energy intervals between the states of non-interacting particles. Since there are many important quantities on a Riemannian manifold, we may define them for $n$-state systems. We define a distance between different equilibrium statistical states of an $n$-state system. We also give a lower bound for the mean square error of an unbiased estimator for the temperature of an $n$-state system.