Accessing the entropy of nonequilibrium steady states

Entropy is one of the key thermodynamic variables reflecting changes in the state of many-particle systems. Unlike other thermodynamic variables, it is well-defined also for nonequilibrium steady states through its relation to information. Applying this relation to physical systems is an ongoing challenge, as it requires knowledge of microscopic high-dimensional continuous distributions which is generally unattainable. A set of new approaches for the measurement of entropy in nonequilibrium steady or absorbing states have been developed and successfully applied to identify dynamic structures and transitions in diverse systems, ranging from jammed packings to swarming bacteria. After a brief review of these approaches we will focus on two methods that give upper bounds for the entropy without sampling microscopic distributions. One uses spatial correlation functions, and the other exploits a recently discovered relation between steady-state entropy and kinetic coefficients. We will demonstrate the validity and usefulness of these methods in several examples of systems far from equilibrium.