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Clock Model at the Verge of Criticality

Alberto Imparato and Marc Suñé publish paper in Physical Review Letters 13. August 2019

[Translate to English:] Vekselvirkende "motorer" i 2D netværk. Illustration fra artiklen.
[Translate to English:] Vekselvirkende "motorer" i 2D netværk. Illustration fra artiklen.

Alberto Imparato and Marc Suñé at IFA have made a theoretical study of the behaviour of interacting "motors" in a 2D grid.

Critical points are quite special points in the phase space of thermodynamic systems. At the critical temperature the system is characterized by large fluctuations  in the local order parameter, for example the local density in a fluid,  such fluctuations being characterized by a slow dynamics.  Similarly the system correlation length, measuring the distance beyond which the behaviour of two small subparts become uncorrelated, diverges.

Furthermore the response to a change in an external thermodynamic force can become significantly large. For example, in a gas at equilibrium with its liquid phase at the critical point a small change in the pressure produces a large density change, corresponding to a diverging compressibility.

Similarly in a system of magnetic atoms, a small change in the external magnetic field gives rise to a large change in the total magnetization,  corresponding to a diverging magnetic susceptibility.

In the present letter we investigated the out-of-equilibrium response of a system of interacting motors, when the out-of-equilibrium disturbance, namely a temperature gradient, is applied on the system, in particular on the system in its critical region.

We introduce an  out-of-equilibrium dynamical response, analogue  to the standard equilibrium response functions, and find that such a response is maximal (although not diverging) when the out-of-equilibrium disturbance is applied around the critical temperature.

The “miles per gallon equivalent” of the system is also maximal in the same regime.

Thus our results show that the critical fluctuations play an important role in enhancing the dynamic and thermodynamic performance of systems of interacting machines.

 The title of the paper is Out-of-Equilibrium Clock Model at the Verge of Criticality