An information and field theoretic approach to the grand canonical ensemble

Abstract: We present a novel derivation of the constraints required to obtain the underlying principles of statistical mechanics using a maximum entropy framework. We derive the mean value constraints by use of the central limit theorem and the scaling properties of Lagrange multipliers. We then arrive at the same result using a quantum free field theory and the Ward identities. The work provides a principled footing for maximum entropy methods in statistical physics, adding the body of work aligned to Jaynes's vision of statistical mechanics as a form of inference rather than a physical theory dependent on ergodicity, metric transitivity and equal a priori probabilities. We show that statistical independence, in the macroscopic limit, is the unifying concept that leads to all these derivations.