When you can’t count, sample!

In statistical mechanics, measuring the number of available states and their probabilities, thus system’s entropy, enables prediction macroscopic properties a physical system at equilibrium. This predictive capacity hinges on knowledge priori probabilities observing system, given by Boltzmann distribution. Unfortunately, successes equilibrium mechanics are hardto replicate out equilibrium, where are, in general, not known, precluding naı̈ve application common tools. last decade, exciting developments have occurred that enable direct numerical estimation entropy density athermal non-equilibrium systems, thanks to significant methodological advances computation volume high-dimensional basins attraction. Here, we provide detailed account these methods, underscoring challenges present such estimations, recent progress matter, promising directions for future work.