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arXiv · 0710.1565

Ballistic Transport at Uniform Temperature

Nawaf Bou-Rabee·Houman Owhadi
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Abstract

A paradigm for isothermal, mechanical rectification of stochastic fluctuations is introduced in this paper. The central idea is to transform energy injected by random perturbations into rigid-body rotational kinetic energy. The prototype considered in this paper is a mechanical system consisting of a set of rigid bodies in interaction through magnetic fields. The system is stochastically forced by white noise and dissipative through mechanical friction. The Gibbs-Boltzmann distribution at a specific temperature defines the unique invariant measure under the flow of this stochastic process and allows us to define ``the temperature'' of the system. This measure is also ergodic and weakly mixing. Although the system does not exhibit global directed motion, it is shown that global ballistic motion is possible (the mean-squared displacement grows like t squared). More precisely, although work cannot be extracted from thermal energy by the second law of thermodynamics, it is shown that ballistic transport from thermal energy is possible. In particular, the dynamics is characterized by a meta-stable state in which the system exhibits directed motion over random time scales. This phenomenon is caused by interaction of three attributes of the system: a non flat (yet bounded) potential energy landscape, a rigid body effect (coupling translational momentum and angular momentum through friction) and the degeneracy of the noise/friction tensor on the momentums (the fact that noise is not applied to all degrees of freedom).

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Nawaf Bou-Rabee, Houman Owhadi. 2007-10-17. Ballistic Transport at Uniform Temperature. https://arxiv.org/abs/0710.1565

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