Understanding how statistical equilibrium can occur in out-of-equilibrium systems is of paramount interest, as it would enable the use of statistical mechanics tools to these systems. Here, we report the first experimental evidence of statistical equilibrium of the large scales of hydroelastic turbulent waves driven by small-scale random forcing. The wave field statistics at scales larger than the forcing scale, resolved in space and time, align well with the predictions of Rayleigh-Jeans equilibrium spectra over more than a decade. We measure zero net energy flux in this regime, as expected. We also determine the effective temperature, entropy, and heat capacity of this nonequilibrium system, demonstrating that classical thermodynamic concepts apply to describe large scales in statistical equilibrium of turbulent systems.

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• Classical statistical mechanics
• Elastic waves
• Hydrodynamic waves
• Waves and free surface flows
• Weak turbulence
• Nonequilibrium systems
• Nonlinear waves
• Data analysis
• Imaging & optical processing