Measuring Entropy in Active-Matter Systems

 



International Conference on Condensed Matter Physics

A tool for estimating the local entropy production rate of a system enables the visualization and quantification of the out-of-equilibrium regions of an active-matter system.


A movie of a molecule jostling around in a fluid at equilibrium looks the same when played forward and backward. Such a movie has an “entropy production rate”—the parameter used to quantify this symmetry—of zero; most other movies have a nonzero value, meaning the visualized systems are out of equilibrium. Researchers know how to compute the entropy production rate of simple model systems. But measuring this parameter in experiments is an open problem. Now Sungham Ro of the Technion-Israel Institute of Technology, Buming Guo of New York University, and colleagues have devised a method for making local measurements of the entropy production rate

[1]. They demonstrate the technique using simulations and bacteria observations

(Fig. 1). The method, which involves comparing forward and time-reversed particle trajectories, could allow researchers to reveal the impact of local entropy production rates on the global dynamics of complex living systems from bacteria to tissues.

Active-matter systems are those composed of energy-consuming agents that exhibit complex collective behavior [2–4].

The classical examples of such agents are birds and fish, which can respectively form flocks that swoop and schools that swirl when they interact in large numbers. Scientists know that these systems break time-reversal symmetry at the single-agent level because of their constant energy consumption [5], and thus active-matter systems have nonzero entropy production rates on the local scale [6].

Scientists also know that active-matter systems break time-reversal symmetry on the global scale, where the agents are observed to collectively organize into patterns—like flocks or schools—whose length scales are much larger than the agents themselves. We don’t, however, know the connection between the global and local breaking of time-reversal symmetry. And simply knowing that the global system has a nonzero entropy production does not tell us much about the system’s behavior. For instance, it tells us how far the system as a whole is from equilibrium, but not where the system is out of equilibrium. Also, we remain in the dark about variations in the system’s thermodynamic properties on intermediate scales. Knowing this information could allow scientists to link the local dynamics of an active-matter system to its global pattern formation, allowing them to use one to predict the other.

To gain this information, scientists have suggested computing local entropy production rates using field-theoretical approaches, but the idea has only been tested for a few specific models [7–9].

Capturing the entropy production rate this way involves collecting “stationary” trajectories (movie frames) from the forward movie and then comparing those frames to ones from the time-reversed movie. This comparison should allow us to quantify regions of the system where nonequilibrium behavior is the most marked. However, accurately quantifying the difference between a stationary trajectory and a time-reversed one is challenging [10].

The work of Ro, Guo, and colleagues takes on this challenge.

For the study, the team considers a generic active-matter system consisting of self-propelled particles that move randomly in space, performing a “persistent” random walk—a specific kind of random walk where particles move in roughly straight lines. They discretize the system on a grid, associating each point of the grid with an integer number that takes on one of a finite set of values, depending on whether there is a particle at that location

 

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