  We propose a Restricted Boltzmann Machine (RBM) neural network using a
quantum thermodynamics formalism and the maximization of entropy as the cost
function for the optimization problem. We verify the possibility of using an
entropy maximization approach for modeling physical systems by applying it to
the Inverse Ising Problem, which describes a system of interacting spins. The
temperature-dependent behaviors of physical quantities, such as magnetization
and Gibbs energy, were calculated from the Ising Hamiltonian whose coefficients
were obtained through entropy maximization and were found to be in good
agreement to literature results. These results suggest that RBM neural networks
using the principle of maximum entropy can be applied to modeling physical
systems that can be described by discrete states, including fundamental quantum
physics such as topological systems, and biological systems such as the
correlated spiking of neurons.
