In a glass of water, oil gathers into droplets: that's equilibrium separation dictated by chemistry. But there are systems where order arises not from rest but from a constant flow of energy. A crowd of people, half of whom are constantly warming up and half freezing, will soon rearrange itself: even if everyone is mixed at first, the hot ones will cluster together, and the cold ones will move aside — simply because heat flows between them.
This is two-temperature phase separation (2-TIPS). Particles bathing in different heat baths spontaneously separate into a dense cold phase and a dilute hot phase. No chemical affinity, just unequal energy input and the resulting heat flow. The review collects examples from soft matter physics: from mixtures of Brownian particles to active colloids, where each particle is a tiny motor converting fuel into motion.
The picture gets more complex. If particles are elongated rather than round, they align into liquid-crystal patterns. Add rotation (chirality)—spiral waves appear. Confine the system in a narrow channel or on a sphere, and geometry rewrites the rules of demixing. Kinetics is also nontrivial: the density of the cold phase affects how fast domains grow. The authors discuss how to bridge the gap from microscopic jumps of individual particles to large-scale flows — through coarse-grained equations.
So from a simple recipe (two kinds of particles, two heaters) nature sculpts an astonishing diversity of structures. By studying this mechanism, we learn to read the nonequilibrium 'cookbook' that governs both living tissues and the self-organizing materials of the future.
Separation due to temperature differences works even without any attraction between particles — only because hot particles collide more often and push the cold ones aside.
In Stephen Baxter's 'Evolution', the temperature difference between ocean layers under Europa's ice generates convection cells where proto-organisms spontaneously arise, a distant echo of 2-TIPS.