Inferring entropy from structure
Gil Ariel
Department of Mathematics, Bar-Ilan University, 52000 Ramat Gan, Israel
Haim Diamant
Raymond and Beverly Sackler School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel
Abstract
The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system’s microstates, which may be prohibitively inefficient to sample or difficult to obtain experimentally. It is beneficial, therefore, to relate the entropy to other integrated properties which are accessible out of equilibrium. We focus on the structure factor, which describes the spatial correlations of density fluctuations and can be directly measured by scattering. The information gained by a given structure factor regarding an otherwise unknown system provides an upper bound for the system’s entropy. We prove that the maximum-entropy model corresponds to an equilibrium system with an effective pair-interaction. Approximate closed-form relations for the effective pair-potential and entropy in terms of the structure factor are obtained. The relations are used to estimate the entropy of an exactly solvable model and numerical examples of systems out of equilibrium, and the results are compared with other entropy-estimation methods. The focus is on low-dimensional examples, where our method, as well as a recently proposed compression-based one, can be tested against a rigorous direct-sampling technique. The entropy inferred from the structure factor is found to be consistent with the other methods, superior for larger system sizes, and accurate in identifying global transitions. Our approach allows for extensions of the theory to more complex systems and to higher-order correlations.
FREE PDF GRATIS: arXiv
