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Chaotic Dynamics in Nonequilibrium Statistical Mechanics

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Encyclopedia of Complexity and Systems Science

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Glossary

Chaotic systems :

The time evolution of a deterministic mechanical system defines a trajectory in the phase space of all the generalized coordinates and generalized momenta. Consider two infinitesimally separated points that lie on two different trajectories in this phase space. If these two trajectories typically separate exponentially with time, the systems is called chaotic provided the set of all points with an exponentially separating partner is of positive measure.

Chaotic hypothesis :

The hypothesis that systems of large numbers of particles interacting with short ranged forces can be treated mathematically as if the system were chaotic with no pathologies in the mathematical description of the systems’ trajectories in phase space.

Dynamical systems theory :

The mathematical theory of the time evolution in phase space, or closely related spaces, of a deterministic system, such as a mechanical system obeying Hamiltonian equations of motion.

Ergodic systems...

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Acknowledgments

I would like to thank Henk van Beijeren for reading a draft of this article and for his very helpful remarks. I would also like to thank Rainer Klages for his new book (Klages 2007), which was very helpful when preparing this article.

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Authors and Affiliations

  1. Institute for Physical Science and Technology and Department of Physics, University of Maryland, College Park, MD, USA

    J. Robert Dorfman

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  1. J. Robert Dorfman
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Correspondence to J. Robert Dorfman .

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  1. Ramtech Ltd., Larkspur, CA, USA

    Robert A. Meyers

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Dorfman, J.R. (2021). Chaotic Dynamics in Nonequilibrium Statistical Mechanics. In: Meyers, R.A. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_66-2

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