Only diversity can lead to synchronisation, say physicists

Exploring a completely new facet of diversity, a group of physicists have empirically demonstrated that within certain systems, the interacting elements can fall in sync only if they are different from each other.

This finding offers a new twist to the previous understanding of how collective behaviour found in nature -- such as fireflies flashing in unison or pacemaker cells working together to generate a heartbeat -- can arise even when the individual insects or cells are different.

Northwestern's Adilson Motter, who led the research, explained that identical entities naturally behave identically -- until they start interacting.

"When identical entities interact, they often behave differently from each other," said Motter, who is a professor of physics in Northwestern's Weinberg College of Arts and Sciences. "But we identified scenarios in which the entities behave identically again if you make them suitably different from each other."

This discovery could help researchers optimize human-made systems, such as the power grid, in which many parts have to remain synchronized while interacting with one another. It also could potentially inform how groups of humans, such as juries, can coordinate to reach a consensus.

This research got published in the journal Nature Physics and was co-authored by Motter alongside Northwestern's Takashi Nishikawa and Ferenc Molnar from Notre Dame University.

This work expands upon Nishikawa's and Motter's 2016 paper, which theoretically predicted the phenomenon.

"It is interesting that systems need to be asymmetric to exhibit behavioural symmetry," said Nishikawa, a research professor of physics in Weinberg. "This is remarkable mathematically, let alone physically. So, many colleagues thought that experimentally demonstrating this effect was impossible."

Motter and his collaborators made the seemingly impossible possible by using three identical electric generators. Each generator oscillated at a frequency of exactly 100 cycles per second. When separated, the identical generators behaved identically.

When connected to form a triangle, their frequencies diverged -- but only until the generators were properly mismatched to have different energy dissipations. At that point, they synchronized again.

"This can be visualized by putting a small lamp between each pair of generators," Molnar explained. "When the generators are identical, the lamp flickers, meaning that the generators are not synchronized. But when the generators' dissipation is tweaked to different levels, the flickering stop, indicating that the generator voltages are oscillating in sync."

The researchers dubbed this phenomenon "converse symmetry breaking" because it represents the opposite of the previously known phenomenon of symmetry breaking, which underlies superconductivity, the Higgs mechanism and even the appearance of zebra stripes.

In symmetry breaking, the dynamical equations have a symmetry that is not observed in the behaviour of the system, while converse symmetry breaking concerns situations in which the behaviour of the system has a given symmetry only when that symmetry is avoided in the dynamical equations.

Motter's team plans to explore the implications of their findings across social, technological and biological systems. In particular, the team is actively working on the design of a power grid that is more stable while allowing incorporation of an increasing share of energy from renewable sources.