The famous experiment of Chladni, wherein sand grains bounce over a vibrated elastic plate, produced a mesmerizing figure that revealed the shape of acoustic eigenmodes to his contemporaries [1]. Some years ago, the same experiment also revealed that Fick's law cannot account for the accumulation of random walkers in places of lesser diffusivity---a natural explanation for the formation of the Chladni figure [2,3]. Using a simpler bouncing-grain experiment, we investigate the thermodynamic consequences of this departure from Fick's law, and cast the Chladni figure in terms of non-equilibrium steady state. The heterogeneity of the figure, indeed, generates a continuous heat flux, which we measure and interpret. Finally, we try to pinpoint what distinguishes the statistics of bouncing grains from those of classical Brownian particles.
[1] E.F.F. Chladni, Entdeckungen über die Theorie des Klanges, Zentralantiquariat der Deutschen Demokratischen Republik (1787).
[2] I. Grabec, Vibration driven random walk in a Chladni experiment, Physics Letters A 381, 59 (2017).
[3] A. Abramian et al., Chladni patterns explained by the space-dependent diffusion of bouncing grains, Physical Review Research 7, L032001 (2025).
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