Experimental evidence for microscopic chaos

Abstract

Many macroscopic dynamical phenomena, for example in hydrodynamics and oscillatory chemical reactions, have been observed to display erratic or random time evolution, in spite of the deterministic character of their dynamics—a phenomenon known as macroscopic chaos1,2,3,4,5. On the other hand, it has been long supposed that the existence of chaotic behaviour in the microscopic motions of atoms and molecules in fluids or solids is responsible for their equilibrium and non-equilibrium properties. But this hypothesis of microscopic chaos has never been verified experimentally. Chaotic behaviour of a system is characterized by the existence of positive Lyapunov exponents, which determine the rate of exponential separation of very close trajectories in the phase space of the system6. Positive Lyapunov exponents indicate that the microscopic dynamics of the system are very sensitive to its initial state, which, in turn, indicates that the dynamics are chaotic; a small change in initial conditions will lead to a large change in the microscopic motion. Here we report direct experimental evidence for microscopic chaos in fluid systems, obtained by the observation of brownian motion of a colloidal particle suspended in water. We find a positive lower bound on the sum of positive Lyapunov exponents of the system composed of the brownian particle and the surrounding fluid.

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Figure 1: Dynamical instability in a Lorentz gas.
Figure 2: Brownian trajectory and power spectrum.
Figure 3: The mean pattern entropy as a function of time.
Figure 4: The entropy per unit time as a function of resolution.

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Acknowledgements

P.G. was supported by the National Fund for Scientific Research (FNRS Belgium); J.R.D. thanks T. Gilbert for helpful remarks, and the US NSF for support; M.E.B. thanks the Physics Department at the University of Utah for support. This work was supported in part by the IUAP/PAI program of the Belgium Government and by the Banque Nationale de Belgique.

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Correspondence to P. Gaspard.

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Gaspard, P., Briggs, M., Francis, M. et al. Experimental evidence for microscopic chaos. Nature 394, 865–868 (1998). https://doi.org/10.1038/29721

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