Kibble-Zurek scaling of the irreversible entropy production

If a system is driven at finite rate through a phase transition by varying an intensive parameter, the order parameter shatters into finite domains. The Kibble-Zurek mechanism predicts the typical size of these domains, which are governed only by the rate of driving and the spatial and dynamical critical exponents. We show that also the irreversible entropy production fulfills a universal behavior, which however is determined by an additional critical exponent corresponding to the intensive control parameter. Our universal prediction is numerically tested in two systems exhibiting noise-induced phase transitions.

Figure 1

Relaxation time $\tau \left(t\right)$ (2) (blue, solid line) and rate of driving $|\dot{\epsilon }/\epsilon |$ (red, dashed line) for $\nu =1$ and $z=3/2$. The vertical lines illustrate the separation of the thermodynamic behavior into adiabatic and impulse regimes [5].

Figure 2

Nonadiabatic entropy production (23) for Eq. (25) with $D=15$, and for a quench from $T_i=8$ to $T_f=4$ (where we have $T_c\simeq 6.19$). The inset is a logarithmic plot (red dots) together with a linear fit (solid, blue line), from which we determine a scaling exponent of 0.78.

Figure 3

Nonadiabatic entropy production (23) for Eq. (27) with $D=15$, and for a quench from $T_i=11$ to $T_f=4.5$ (where we have $T_c\simeq 7.91$). The inset is a logarithmic plot (red dots) together with a linear fit (solid, blue line), from which we determine a scaling exponent of 0.81.