The large deviation principle (LDP) is the main hypothesis of Varadhan's theorems ([3], [4]), which provide an effective method for investigating the asymptotic behaviour of some integrals. In equilibrium statistical mechanics the limiting specific free-energy can be estimated by using this method. In the case of quantum spin systems interacting with another quantum system, the LDP was employed in [1] to obtain upper and lower bounds for the free-energy. For further applications see [2]. The purpose of this paper is to give a topological criterion for a sequence of probability measures to satisfy the large deviation principle. We will prove that it is enough to check the conditions defining the LDP for sets from a suitable base for topology. As a corollary, we will derive the LDP for product measures (see also [1]). Finally, we will illustrate the use of the LDP3 for product measures in statistical thermodynamics by describing the maximum entropy principle in R2.

Criterion for the large deviation principle

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Criterion for the large deviation principle