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Entropy 2004, 6(1), 57-67; doi:10.3390/e6010057

Langevin approach to the Porto system

*  and
Institute of Physics of Charles University, Faculty of Mathematics and Physics, Ke Karlovu 5, CZ-121 16 Prague 2, Czech Republic
* Author to whom correspondence should be addressed.
Received: 24 June 2003 / Accepted: 15 December 2003 / Published: 12 March 2004
(This article belongs to the Special Issue Quantum Limits to the Second Law of Thermodynamics)
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M. Porto (Phys. Rev. E 63 (2001) 030102) suggested a system consisting of Coulomb interacting particles, forming a linear track and a rotor, and working as a molecular motor. Newton equations with damping for the rotor coordinate on the track x, with a prescribed time-dependence of the rotor angle Θ, indicated unidirectional motion of the rotor. Here, for the same system, the treatment was generalized to nonzero temperatures by including stochastic forces and treating both x and Θ via two coupled Langevin equations. Numerical results are reported for stochastic homogeneous distributions of impact events and Gaussian distributions of stochastic forces acting on both the variables. For specific values of parameters involved, the unidirectional motion of the rotor along the track is confirmed, but with a mechanism that is not necessarily the same as that one by Porto. In an additional weak homogeneous potential field U(x)=const.x acting against the motion, the unidirectional motion persists. Then the rotor accumulates potential energy at the cost of thermal stochastic forces from the bath.
Keywords: Porto system; molecular motor Porto system; molecular motor
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Bok, J.; Cápek, V. Langevin approach to the Porto system. Entropy 2004, 6, 57-67.

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