Can flocks of birds be described as a gas of particles in equilibrium?

When a flock of birds fly in the sky they almost seem like a fluid that moves in the air. The movement of a collection of bacteria can also be remarkably similar to the movement of a liquid or gas. What about stampeding buffalo herds? Look at them from a distance (waking side by side with a herd of buffalo is probably not a good idea) and you will see that they also bear a striking resemblance to a gas of particles. And for a physicist this resemblance was too strong to be ignored! They stated studying these systems, that came to be known as active matter, using the same tools they would use to study a gas of particles.

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Figure 1. A flock of birds are an example of active matter.

Active matter systems are large assemblies of individual unities (birds, bacteria, buffalos) that dissipate energy. As the birds fly in the air, for example, they use energy to produce mechanical work. This constant consumption of energy is what brings the “active” to active matter and is what makes it so challenging to study them.

A (non-active) gas of particles can be described and understood using thermodynamics and statistical physics. If this gas is in equilibrium, then equilibrium statistical physics can be used to model them. Active matter is, by it’s own definition, out of equilibrium. The particles consume energy constantly and therefore are constantly changing the inner properties of the matter. In spite of that, physicists have been quite successful at modeling active matter using tools and concepts of equilibrium statistical physics, such as pressure and temperature. But the limits of this application are heavily debated.

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Figure 2. Can active matter be described by equilibrium statistical mechanics?

When the birds interact with each other, for example, a collective behavior can emerge that is unlike anything possible with an equilibrium system. However, it can be quite challenging to identify precisely the signature of non-equilibrium physics in their emerging properties. Pinpointing when non equilibrium properties arise is essential to fully understand and describe the behavior of active matter.

In order to better learn when equilibrium physics can or cannot be applied to active matter, Étienne Fodor from the University of Paris Diderot (France), and colleagues, analyzed an active matter model consisting of self propelled particles. They used theoretical tools to evaluate the behavior of this system.

The model consists of self-propelled particles that are constantly moving and dissipating their energy through the interaction with a surrounding fluid. By changing the parameters of the model it is possible to obtain particles with different “persistent times”. This corresponds to the time it would take for the particle motion to appear random. When the persistence time is close to zero the motion appears random rather than directed. They behave like particles moving in a liquid, changing the direction of the movement due to the collision with the molecules in the fluid (Brownian motion). This is a situation that can be described using equilibrium statistical physics. When the persistent times are very long then it is possible to observe truly non-equilibrium effects. Particles with an intermediate persistence time are more difficult to deal with. Are they random or not?

Fodor and colleagues found that for intermediate persistence times the system is in an effective equilibrium. They have features of an equilibrium system, such as reversible dynamics for the particles and no entropy production. However they cannot be described via a Boltzmann distribution, which is used to describe systems in thermal equilibrium. According to the tests done by the scientists, equilibrium concepts and methods can be employed in this intermediate regime but the system is not in a thermal equilibrium.

Other self-propelled particle models still need to be evaluated to determine if the researchers’ findings are general. However, the team’s analysis already provides preliminary guidelines for when equilibrium statistics can be used to describe an active matter system.

By Kellen Manoela Siqueira

The full paper can be found in the July 2016 edition of Physics Review Letter.

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