Phase transitions are typically accompanied by changes in an order parameter. Sometimes the right parameter to describe one of those changes is obvious, such as density in a liquid–gas transition or net magnetization in a ferromagnet. But in many systems, particularly those far from equilibrium, the right parameterization is unknown.
In their recent paper, Stefano Martiniani and Paul Chaikin from New York University and Dov Levine from Technion–Israel Institute of Technology in Haifa used a lossless file compression algorithm to quantify order and observe phase transitions in simulated systems whose particles interact and generate nonequilibrium dynamics. Such algorithms use as little data as possible to fully describe the information contained in a file. The computable information density (CID)—the ratio of the compressed data string length to the original data string length—can serve as a proxy for entropy, which cannot be explicitly calculated for out-of-equilibrium systems.
The researchers started by considering a one-dimensional conserved lattice gas (CLG). They placed N particles among L (L ≥ N) sites on a line, as shown in the figure. If a particle’s neighboring site was occupied, the particle was active (shown in red) and got moved to an unoccupied neighboring site; otherwise, it stayed put. If half or fewer of the sites were occupied, the CLG eventually reached a stationary state in which no particles were active. At N/L = 0.5, a phase transition occurred, above which the dynamics persisted in an active state indefinitely.
The analysis showed unexpected ordering in the CLG: Based on their CID, absorbing states reached dynamically were more ordered than those reached by random sampling, particularly as the system approached the phase transition. Two-dimensional models, one with and one without a lattice, showed the same increased order in dynamically obtained absorbing states seen in the 1D CLG model.
Martiniani and coworkers also applied their analysis to simulations of 2D active Brownian particles that do not have an inactive state. The entropy-tracking CID decreased when the particles separated into liquid-like and gas-like phases at a total area fraction of 0.37, thereby increasing their order. In agreement with theoretical predictions, a discontinuity in the CID indicates that the transition is first order. Now that its utility has been demonstrated, the CID approach may also be used to characterize order and phase behavior in experimental data of active particles or glassy systems whose entropy cannot be computed. (S. Martiniani, P. M. Chaikin, D. Levine, Phys. Rev. X 9, 011031, 2019. Thumbnail image credit: Bernd Luz, CC BY-SA 3.0.)