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Ballistic Transport at Uniform Temperature

Bou-Rabee, Nawaf and Owhadi, Houman (2007) Ballistic Transport at Uniform Temperature. . (Submitted)

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A paradigm for isothermal, mechanical rectification of stochastic uctuations 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 strongly 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^2). 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 at (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).

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Owhadi, Houman0000-0002-5677-1600
Additional Information:(Submitted on 8 Oct 2007 (v1), last revised 17 Oct 2007 (this version, v2). 17 February 2013.
Record Number:CaltechAUTHORS:20160224-101438724
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64730
Deposited By: Ruth Sustaita
Deposited On:24 Feb 2016 19:12
Last Modified:03 Oct 2019 09:40

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