Rock-paper-scissors game reveals new thermal transport phenomenon: Robust temperature localization and topological phase transition

In passive thermal diffusion systems, heat tends to spread uniformly, eventually reaching thermal equilibrium. However, the introduction of active control mechanisms can fundamentally alter this behavior. Inspired by the cyclic rock-paper-scissors competition in ecosystem, a research team led by Professor Run Hu at Huazhong University of Science and Technology has discovered a novel thermal transport phenomenon. The researchers found that under specific modulation parameters, heat continuously accumulates toward one boundary, forming a robust temperature localization phenomenon, which exhibits remarkable robustness against external disturbances and topological transition.

In ecosystems, the rock-paper-scissors model describes a cyclic competitive relationship among species. Take the side-blotched lizard as an example: orange-throated males (rock) dominate blue-throated ones (scissors), blue-throated males dominate yellow-throated ones (paper), and yellow-throated males dominate orange-throated ones, forming a dynamic cycle. Extending this concept to thermal transport, researchers connected multiple thermal sites with Peltier modules to construct a one-dimensional thermal rock-paper-scissors chain. By carefully regulating the direction and magnitude of active thermal transport, this work established a cyclic heat transfer pathway analogous to biological cyclic competition and introduced the skewness parameter R to control the asymmetry of heat transport.

In this actively controlled thermal system, the uniformly distributed state predicted by conventional diffusion theory did not emerge. Numerical simulations revealed a striking phenomenon: when the skewness deviates from its balanced value R=1, heat no longer spreads evenly but continuously accumulates toward one end of the chain, forming a robust temperature localization profile. When R<1, heat localizes at the right boundary; when R>1, it localizes at the left boundary. Remarkably, this localization is highly robust. It persists even when the system's parameters are randomly disturbed or when extra, unplanned connections are added, much like an ecosystem facing external pressures. In other words, the direction of temperature localization depends solely on whether the skewness R is greater than or less than 1.

In-depth topological band theory analyses on generalized Brillouin zone and real space Hamiltonian uncovered the physical essence behind this phenomenon: a topological phase transition. At the perfectly balanced critical point R=1, the system is uniform. Once deviating from this point, the system enters two distinct topological phases, corresponding to heat localization at the left or right boundary. This phase transition can be clearly characterized by the winding number, which is a topological invariant marking a fundamental change in the system's topological properties. It is 0 when R=1, and −1 and +1 when R<1 and R>1 respectively. This indicates a complete change in the topological properties of the system when it crosses the critical point R=1, which is known as a topological phase transition.

"This research integrates ecological competition concepts with topological physics and extends them into thermal science, discovering a novel phenomenon in actively controlled thermal transport systems," said Professor Run Hu, corresponding author of the paper. "This discovery reveals hidden topological behavior in active thermal transport systems, providing a new perspective for the study of non-equilibrium heat transport, expanding the research scope of topological heat physics, and opening up new directions for advanced active heat regulation and thermal management."

The ability to robustly steer and localize heat on demand could lead to a new generation of thermal management solutions. Potential applications include highly efficient thermal shielding for sensitive electronics, more effective waste heat harvesting systems, or even novel thermal logic devices for computing.

Huazhong University of Science and Technology is the first completing institution of this research. PhD student Zhaochen Wang is the first author, and Professor Run Hu is the corresponding author. This work was supported by the National Key Research and Development Program of China and the National Natural Science Foundation of China.

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