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Cubic energy materials such as thermoelectrics or hybrid perovskite materials are often understood to be highly disordered1,2. In GeTe and related IV–VI compounds, this is thought to provide the low thermal conductivities needed for thermoelectric applications1. Since conventional crystallography cannot distinguish between static disorder and atomic motions, we develop the energy-resolved variable-shutter pair distribution function technique. This collects structural snapshots with varying exposure times, on timescales relevant for atomic motions. In disagreement with previous interpretations3–5, we find the time-averaged structure of GeTe to be crystalline at all temperatures, but with anisotropic anharmonic dynamics at higher temperatures that resemble static disorder at fast shutter speeds, with correlated ferroelectric fluctuations along the <100>cdirection. We show that this anisotropy naturally emerges from a Ginzburg–Landau model that couples polarization fluctuations through long-range elastic interactions6. By accessing time-dependent atomic correlations in energy materials, we resolve the long-standing disagreement between local and average structure probes1,7–9and show that spontaneous anisotropy is ubiquitous in cubic IV–VI materials.

Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity occurs, for instance, in active matter1–6, non-equilibrium systems7–9, networks of neurons10,11, social groups with conformist and contrarian members12, directional interface growth phenomena13–15and metamaterials16–20. Although wave propagation in non-reciprocal media has recently been closely studied1,16–20, less is known about the consequences of non-reciprocity on the collective behaviour of many-body systems. Here we show that non-reciprocity leads to time-dependent phases in which spontaneously broken continuous symmetries are dynamically restored. We illustrate this mechanism with simple robotic demonstrations. The resulting phase transitions are controlled by spectral singularities called exceptional points21. We describe the emergence of these phases using insights from bifurcation theory22,23and non-Hermitian quantum mechanics24,25. Our approach captures non-reciprocal generalizations of three archetypal classes of self-organization out of equilibrium: synchronization, flocking and pattern formation. Collective phenomena in these systems range from active time-(quasi)crystals to exceptional-point-enforced pattern formation and hysteresis. Our work lays the foundation for a general theory of critical phenomena in systems whose dynamics is not governed by an optimization principle.