Abstract
We examine the Jarzynski equality for a quenching process across the critical point of second-order phase transitions, where absolute irreversibility and the effect of finite-sampling of the initial equilibrium distribution arise in a single setup with equal significance. We consider the Ising model as a prototypical example for spontaneous symmetry breaking and take into account the finite sampling issue by introducing a tolerance parameter. The initially ordered spins become disordered by quenching the ferromagnetic coupling constant. For a sudden quench, the deviation from the Jarzynski equality evaluated from the ideal ensemble average could, in principle, depend on the reduced coupling constant ε0 of the initial state and the system size L. We find that, instead of depending on ε0 and L separately, this deviation exhibits a scaling behavior through a universal combination of ε0 and L for a given tolerance parameter, inherited from the critical scaling laws of second-order phase transitions. A similar scaling law can be obtained for the finite-speed quench as well within the Kibble-Zurek mechanism.
Highlights
Fluctuation theorems (FTs) provide universal and exact relations for nonequilibrium processes irrespective of how far a system is driven away from equilibrium
FTs provide a unique way to evaluate the free energy difference ΔF between equilibrium states through nonequilibrium processes[3], which could be useful for systems such as complex molecules[9,10] that take a very long time to reach an equilibrium state
Sufficient sampling of the dominant realizations becomes intractable with increasing system size, and in reality the Jarzynski equality (JE) is hard to verify to high accuracy with a finite number of samples
Summary
Production in Critical Systems received: 21 January 2016 accepted: 20 May 2016 Published: 09 June 2016. We examine the Jarzynski equality for a quenching process across the critical point of second-order phase transitions, where absolute irreversibility and the effect of finite-sampling of the initial equilibrium distribution arise in a single setup with equal significance. Using the scaling theory of phase transitions and numerical simulations, the deviation from the ideal ensemble average JE, i.e., the ensemble average of e−σ using infinite number of samples, is examined as a function of the system size and the reduced coupling constant. It exhibits a universal scaling behavior inherited from the critical scaling of the correlation length and the relaxation time in second-order phase transitions.
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