Students of thermodynamics learn that closed systems tend toward states of increasing entropy, which is often considered synonymous with decreasing order. But in some systems, entropy and order can be allies, not opponents: The systems tend toward greater order as—and precisely because—their entropy increases.
The phenomenon isn’t as paradoxical as it sounds. The secret is to partition the system’s degrees of freedom into two subsets, so that ordering in one subset increases the entropy of the other—and thus of the system as a whole. The trick is well known in soft-matter physics, where entropy-driven order shows up in contexts such as colloidal crystallization: When an ensemble of particles assembles from a disordered dispersion into an ordered lattice, each one can have more room to move around.
The mechanical motion of colloidal particles involves continuous degrees of freedom, which can be complicated to model and difficult to precisely measure. Now Yale...
