Universal U(1) Ordering Far from Equilibrium

In the long-wavelength limit, emergent behaviour is often insensitive to the messy microscopic details. This universality allows physically distinct systems to exhibit the same collective dynamics, governed only by a small set of symmetries, conservation laws, and effective degrees of freedom. In this talk, we explore how a global U(1) symmetry under coarse-graining gives rise to universal stochastic phase dynamics in driven-dissipative systems. We illustrate this in two very different settings: bosonic gases and pattern formation in biological cells. First, we discuss phase ordering in a driven-dissipative photon gas. Although Hamiltonian interactions are negligible, coupling to a molecular reservoir supports a Berezinskii–Kosterlitz–Thouless-like transition at finite lengthscales, tuneable from strongly non-equilibrium to equilibrium-like behaviour. At longer scales, the phase obeys a noisy Kuramoto–Sivashinsky equation, whose asymptotic dynamics lies in the Kardar–Parisi–Zhang universality class. We examine how this KPZ physics competes with vortex-driven ordering and why it does not control the transition on accessible scales. We then turn to chemically coupled cellular systems, where increasing cell density drives collective oscillations through a diffusing signalling field. Coarse graining yields a compact stochastic phase field, allowing phase ordering, topological defects, and Kibble–Zurek dynamics. Together, these examples show how microscopically distinct systems can flow towards closely related stochastic U(1) dynamics far from equilibrium.