Entropy from Machine Learning

Subsequently, one can use virtually any machine learning classification algorithm for computing entropy. This procedure can be used to compute entropy, and consequently the free energy directly from a set of Monte Carlo configurations at a given temperature. As a test of the proposed method, using an off-the-shelf machine learning classifier we reproduce the entropy and free energy of the 2D Ising model from Monte Carlo configurations at various temperatures throughout its phase diagram. Other potential applications include computing the entropy of spiking neurons or any other multidimensional binary signals. 1 Introduction The problem of estimating entropy of high dimensional binary configurations or signals is ubiquitous in many disciplines. In physics, we very often have at our disposal a set of configurations of some physical system generated by a Monte Carlo simulation at a given temperature T 0. This data is very much geared towards computing expectation values of various operators or their correlation functions, however obtaining the entropy or free energy of the system is far from trivial. Indeed, to the best of our knowledge, there is no known way to compute the entropy directly from these configurations even for a system of a quite moderate size (e.g. for a 20 20 lattice). The goal of the present paper is to propose machine email: romuald.janik@gmail.com