Towards Approximation of Equilibrium States in Nonadditive Lattice Systems

Abstract

We propose a framework for solving the problem of approximation of equilibrium-like like states in one-dimensional classical lattice systems with superadditive Hamiltonians. Systems of this type arise naturally in the generalisation of thermodynamic formalism dealing with the dynamics generated by nonconformal maps, [4,5]. It is known that although a generalised version of variational principle holds for such systems, equilibrium states may not exist in general. Our approach is to characterise approximately equilibrium states by linear functionals bounded by free energy on a suitable Banach space of Hamiltonians. We construct a map binding states on the algebra of observables with linear functionals on the space of (nonadditive) Hamiltonians and study its basic properties.