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|Can we get work out of unbiased fluctuation? It is possible for
macroscopic fluctuations. However, the situation is more subtle for
microscopic fluctuations. We know from the second law of thermodynamics
that is is impossible to get work in a repetitive cyclic manner from a
single heat bath at equilibrium. But nothing forbids the appearance of
Maxwell demon in the case of nonequilibrium fluctuations. Then, it is
possible to construct Brownian motors which are driven by microscopic
nonequilibrium fluctuations. Such motors may be found in biological
systems operating far from equilibrium.
Recently, various mathematical models of Brownian motors have been investigated. Some of them show remarkable properties such as negative mobility. In the following we introduce our own model. See References for other models.
Consider a globally coupled system of N particles with state-dependent noise (multiplicative noise):
In order to produce flux, other models necessarily use a asymmetric potential (ratchet potential) or potential fluctuation with a finite correlation in time. Our model has neither spacial nor temporal bias but nevertheless it produces flux. How can it happen? A key point is that the system undergoes noise-induced nonequilibrium phase transition and reflection symmetry of the system is spontaneously broken. (See Figure 1 and movie) As a result the particles experiences effectively a ratchet-like potential. Figure 2 illustrates a phase diagram.
The response properties of this model is very interesting. If uniform force applied to the system in the symmetry-broken phase, anomalous hysteresis is observed (See Figure 3). Even more interestingly, if the force is applied to the system just outside the symmetry-broken region, the current flows in the opposite direction to the force. (negative zero-bias mobility, See Figure 4).
When many Brownian particles driven by multiplicative noise are coupled, many interesting phenomenon are induced through non-equilibrium phase transition and breaking of ergodicity. The coupled Brownian motor is one example. More intersting phenomenon are to be discovered.
Quicktime movie(1Mb) of a steady state.