Deep learning of thermodynamic laws from microscopic dynamics

We numerically show that a deep neural network (DNN) can learn macroscopic thermodynamic laws purely from microscopic data. Using molecular dynamics simulations, we generate the data of snapshot images of gas particles undergoing adiabatic processes. We train a DNN to determine the temporal order of input image pairs. We observe that the trained network induces an order relation between states consistent with adiabatic accessibility, satisfying the axioms of thermodynamics. Furthermore, the internal representation learned by the DNN acts as an entropy. These results suggest that machine learning can discover emergent physical laws that are valid at scales far larger than those of the underlying constituents---opening a pathway to data-driven discovery of macroscopic physics.