Non-equilibrium steady state of stochastic circuits ()

Doron Cohen

The study of systems with non-equilibrium steady state (NESS) has become of great interest in recent years. The paradigm for NESS is a system which is coupled to two equilibrated reservoirs "A" and "B" that are characterized by different temperatures \( T_A \) and \( T_B \) . The steady state of the system is not canonical. A particular case of special interest is having one reservoirs (call it "A") that is replaced by a stationary driving source, while the relaxation is provided by a bath (call it "B") that has some finite temperature \( T_B \) . This is still the same paradigm because formally the driving source "A" can be regarded as a bath that has an infinite temperature \( T_A=\infty \) .

A prototype model system is illustrated in the above figure: a ring that is made up of N isolated sites with on site energies \( E_n \) . The ring is coupled to a heat reservoir (represented by the blue "environment") and subjected to a noisy driving field (represented by the red circle) that induces a current in the ring. In the figure below the current is plotted as a function of the scaled driving intensity and imaged for various strengths ("sigma") of disorder. The right panel demonstrates the statistics of the current over many realizations of the disorder.

More recently we have we have addressed questions that concern the relaxation of such currents, and how the relaxation depends on percolation and localization properties of the model. Currently we are trying to extend the theory, considering general stochastic active networks.

The ring model belongs to a class of "glassy" systems for which the rate of energy absorption is a semi-linear (rather than linear) functional with respect to the power spectrum of the driving source. This is due to the percolation-like nature of the dynamics. We have demonstrated that a weak coupling to a bath would lead in such case to a novel non-canonical steady state that has glassy characteristics. Furthermore, we have discovered a related quantum saturation effect that sets an upper limit on the NESS temperature, irrespective of the driving intensity.

For references see: http://www.bgu.ac.il/~dcohen/#refsNonEq
For more highlights see: http://physics.bgu.ac.il/~dcohen/HOMEPAGE/Highlights.html