3,072 research outputs found
Ergodic solenoids and generalized currents
We introduce the concept of solenoid as an abstract laminated space. We do a
thorough study of solenoids, leading to the notion of ergodic and uniquely
ergodic solenoids. We define generalized currents associated with immersions of
oriented solenoids with a transversal measure into smooth manifolds,
generalizing Ruelle-Sullivan currents.Comment: 28 pages, 2 figures. Fully revised presentation of the paper.
Accepted in Revista Matematica Complutense. The final publication is
available at http://www.springerlink.co
Ergodic solenoidal homology: density of ergodic solenoids
A measured solenoid is a laminated space endowed with a tranversal measure
invariant by holonomy, as defined in arXiv:0910.2836. A measured solenoid
immersed in a smooth manifold produces a closed current (known as generalized
Ruelle-Sullivan current). Uniquely ergodic solenoids are those for which there
is a unique (up to scalars) transversal measure. By the results in
arXiv:0910.2913, for any smooth manifold, any real homology class is
represented by a uniquely ergodic solenoid. In this paper, we prove that the
currents associated to uniquely ergodic solenoids are dense in the space of
closed currents, therefore proving the abundance of such objects.Comment: 9 pages, 2 figure
Heating without heat: thermodynamics of passive energy filters between finite systems
Passive filters allowing the exchange of particles in a narrow band of energy
are currently used in micro-refrigerators and energy transducers. In this
letter, we analyze their thermal properties using linear irreversible
thermodynamics and kinetic theory, and discuss a striking phenomenon: the
possibility of increasing or decreasing simultaneously the temperatures of two
systems without any supply of energy. This occurs when the filter induces a
flow of particles whose energy is between the average energies of the two
systems. Here we show that this selective transfer of particles does not need
the action of any sort of Maxwell demon and can be carried out by passive
filters without compromising the second law of thermodynamics. The phenomenon
allows us to design cycles between two reservoirs at temperatures
that are able to reach temperatures below or above .Comment: 5 pages, 3 figure
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