Turbulence That Refuses to Thermalize: A Reversible Dance in Optical Fibers
26 Dec 2025, Yanjiang
What do you do when you encounter something that wants to be both an orderly snowflake and a hurricane at the same time? For most of us, this is a riddle for a party. For T. Torres and colleagues, it became the central puzzle behind a new study of wave turbulence in optical fibers.
Turbulence is nature’s destroyer of structure. Stir a pot of soup, and any pattern you had is soon homogenized into a uniform broth. In physics, this process—thermalization—is the ultimate end point: energy evenly distributed, entropy maximized, everything boringly democratic. But a team led by G. Millot has now discovered that in a carefully prepared system of light waves, turbulence can take a different path. Instead of marching irreversibly toward thermal death, the waves can spontaneously organize into a fast, reversible oscillatory dance—a regime mediated by what physicists call anomalous correlators.
Their work, appearing as a preprint (arXiv:2512.17777), combines theoretical wave turbulence theory with experiments in optical fibers to reveal two fundamentally distinct turbulent regimes. The first is the expected slow march toward thermal equilibrium, described by the wave turbulence kinetic equation and the associated H-theorem of entropy growth. The second, far more surprising, is a regime where strong phase correlations emerge spontaneously, leading to a reversible exchange of energy between different polarization states—a process that is efficient, oscillatory, and anything but thermal.
This is not a metaphor of waves being “stubborn” or “creative”; it is a precise mathematical consequence of the underlying Hamiltonian structure of the system, as we shall see.
The Two Faces of Turbulence
To understand why these two regimes exist, we need to step inside the experiment. The team uses an optical fiber—a long, thin strand of glass—through which they send laser light. The light’s polarization (the direction in which its electric field oscillates) evolves as it travels, governed by two coupled nonlinear Schrödinger equations. This system is Hamiltonian, meaning it conserves total energy in principle, but it can still redistribute energy among different modes of the field.
Think of it like an investment portfolio, where you have a mix of safe bonds and risky stocks. The standard approach in wave turbulence theory predicts that over time, the portfolio (the wave system) will thermalize—the energy will spread evenly across all “accounts” (wave modes), leading to maximum entropy. This is the irreversible thermalization regime, well described by the wave turbulence kinetic equation and its H-theorem, which guarantees entropy increase.
But the team found something else. Under certain conditions—specifically, when the nonlinear coupling between polarization components is strong enough, and the initial power imbalance between the axes is present—the system refuses to thermalize. Instead, it enters a reversible oscillatory regime. The anomalous correlator, a quantity that measures phase correlations between the two polarization components, grows exponentially from initially negligible levels, and then the system begins to oscillate. The energy sloshes back and forth between the two polarization axes like a pendulum, never settling down.
This parallel narrative of irreversible thermalization and reversible dynamics is an effective tool the team uses to reveal a deeper truth about wave turbulence: it is not a single process, but a family of behaviors that depend on the initial conditions and the strength of the underlying interactions.
The Anomalous Correlator: A Secret Language
What exactly is this “anomalous correlator”? In everyday language, it measures the degree to which the two polarization components have become “phase-locked”—their waves are no longer independent, but have begun to coordinate their ups and downs. In the thermalization regime, the phase correlations are negligible; the two components are like strangers on a bus, each minding their own business. In the reversible regime, they start exchanging signals, and soon they are dancing in perfect synchrony, trading energy back and forth.
The team’s theoretical framework shows that this anomalous correlator can be described by a closed set of equations—the anomalous correlator kinetic equation (AC-KE)—which predicts exponential growth followed by periodic oscillations. Numerical simulations of the full nonlinear Schrödinger equations confirm this behavior, and experimental measurements with highly sensitive polarimeters and spectrum analyzers match the theoretical predictions with remarkable fidelity. For instance, when the input power is raised to a level where the nonlinear length becomes shorter than the fiber length, the team observes clear signatures of these reversible oscillations: the power difference between the two polarization axes oscillates, and the anomalous correlator itself shows a clear periodic exchange.
This is not a metaphor; it is a precise mathematical statement, confirmed by the team’s measurements and simulations. But what does it mean for our understanding of turbulence?
The implications are profound. For decades, the wave turbulence community has focused almost exclusively on irreversible thermalization—the slow, statistical approach to equilibrium described by kinetic equations and H-theorems. This new work shows that the Hamiltonian structure of the system allows for a completely different kind of behavior: coherent, reversible dynamics that arise from the same underlying equations. It suggests that turbulence is not a one-way street to disorder; under the right conditions, it can become a structure-building process, creating phase correlations and oscillatory energy transfers that defy the usual thermodynamic arrow.
From Optical Fibers to the Universe
Why should anyone beyond the narrow world of nonlinear optics care? Because the equations that govern light in optical fibers—the nonlinear Schrödinger equation—appear in a wide range of physical contexts, from Bose-Einstein condensates to ocean waves, from plasma physics to gravitational wave astronomy. Any system described by coherently coupled wave equations could, in principle, exhibit these two regimes.
The team’s experimental realization in optical fibers is a proof of principle: they have shown that reversible turbulent dynamics are not a theoretical curiosity but a physically realizable phenomenon. Their results also open a new window for controlling wave systems. If you can tune the parameters to push the system into the reversible regime, you might be able to manipulate energy transfer in a way that is both fast and predictable—like a switchable heat exchanger that can either homogenize energy or oscillate between states.
This is not to say we will soon have “turbulence engines” in every lab. The conditions required are specific: a strong enough nonlinearity, a suitable initial power imbalance, and a system length that allows the exponential growth of the anomalous correlator. But the team’s theoretical framework provides clear guidelines for finding these conditions in other systems.
The Road Ahead
The team is already looking ahead. Their work raises a natural question: can similar reversible regimes be observed in other wave systems, such as in Bose-Einstein condensates or in deep water waves? The nonlinear Schrödinger equation is universal in its applicability, but the specific coupling mechanism—the coherent coupling between polarization components in an optical fiber—has analogues in other physical systems. For instance, in spinor Bose-Einstein condensates, the internal spin degrees of freedom can play a role similar to polarization.
More broadly, this work challenges the standard narrative of wave turbulence as a purely irreversible process. It shows that the Hamiltonian nature of the system imposes constraints that, under certain conditions, can lead to coherent, reversible dynamics. The same mathematics that underlies the irreversible H-theorem also allows for the emergence of spontaneous phase correlations that defy thermalization.
Perhaps one day, when physicists want to understand the behavior of nonlinear waves in the cosmos—from the early universe to neutron star mergers—they will need to consider not just irreversible thermalization, but also the possibility of reversible coherent structures mediated by anomalous correlators. For now, the team’s work stands as a beautiful demonstration that turbulence, far from being the destroyer of all order, can also be the seed of a strange and graceful dance.
Yanjiang is an online editor of Loom Science
References
- T. Torres et al., Irreversible thermalization vs reversible dynamics mediated by anomalous correlators: Wave turbulence theory and experiments in optical fibers, arXiv:2512.17777