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Nonlinear phenomena are phenomena, which, in contrast to a linear system, cannot be explained by a mathematical relationship of proportionality (that is, a linear relationship between two variables). For example, the spread of an infectious disease is most often exponential, rather than linear, with time.
The hydrodynamic description of many-body quantum systems is a key part of our understanding of out-of-equilibrium physics. Exotic, highly constrained quantum particles called fractons require a treatment that goes beyond hydrodynamics.
Thermodynamic concepts can be used to understand nonlinear wave systems, but direct evidence for these analogies is scarce. Experiments with multimode fibres have now enabled direct measurement of the thermalization process of optical waves.
