The work began not with birds or neurons, but with quantum weirdness. “I believe their work represents rich territory for mathematical development,” said Robert Kohn of the Courant Institute of Mathematical Sciences at New York University. The new work also draws connections among a range of areas and phenomena that, for years, haven’t seemed to have anything to say to each other. “So you can bring all the machinery that we already have about exceptional points to study these systems.” ![]() “That’s what no one has thought about before, using these in the context of nonequilibrium systems,” said the physicist Cynthia Reichhardt of Los Alamos National Laboratory in New Mexico. But they’ve never been associated so generally with this type of phase transition. Exceptional points aren’t new physicists and mathematicians have studied them for decades in a variety of settings. Now the team has found that these exceptional points also control phase transitions in nonreciprocal systems. At an exceptional point, the mathematical behavior of a system differs dramatically from its behavior at nearby points, and exceptional points often describe curious phenomena in systems - like lasers - in which energy is gained and lost continuously. Generally, an exceptional point in a system is a singularity, a spot where two or more characteristic properties become indistinguishable and mathematically collapse into one. Vitelli and his colleagues see an answer in mathematical objects called exceptional points. ![]() How can we analyze phases in such ever-changing systems? But all these extra energy sources and mismatched reactions make for a complex dynamical system beyond the reach of statistical mechanics. Many of these systems are kept out of equilibrium because individual constituents have their own power source - ATP for cells, gas for cars. Engineers and physicists who work with metamaterials - which get their properties from structure, rather than substance - have harnessed nonreciprocal elements to design acoustic, quantum and mechanical devices. Cars barreling down a highway or stuck in traffic are similarly nonreciprocal. So bird A doesn’t interact with bird B in the same way that bird B interacts with bird A it’s not reciprocal. Flocking birds show how easily the law is broken: Because they can’t see behind them, individuals change their flight patterns in response to the birds ahead of them. Out of equilibrium, nonreciprocity dominates. Predators eat prey, for example, but prey doesn’t eat its predators.įor these unruly systems, statistical mechanics falls short in representing phase transitions. “Imagine two particles,” said Vincenzo Vitelli, a condensed matter theorist at the University of Chicago, “where A interacts with B in a different way than how B interacts with A.” Such nonreciprocal relationships show up in systems like neuron networks and particles in fluids and even, on a larger scale, in social groups. ![]() In such systems, Newton’s third law becomes moot. A human body that settles into equilibrium is a dead body. We’re kept out of equilibrium by our metabolism, which converts matter into energy. Perhaps the most glaring example is life itself. This allows researchers to fully model the conditions that give rise to phase transitions in matter, when one state of matter transforms into another, such as when water freezes.īut many systems exist and persist far from equilibrium. Mathematically, these systems are elegantly described with statistical mechanics, the branch of physics that explains how collections of objects behave. When a system is in equilibrium, no energy goes in or out and such reciprocity is the rule. It’s been reassuring us for 400 years, explaining why we don’t fall through the floor (the floor pushes up on us too), and why paddling a boat makes it glide through water. Newton’s third law tells us that for every action, there’s an equal reaction going the opposite way.
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