Critical dynamics of one-dimensional irreversible systems

M. P. Kawatra, J. I. Budnick

Fernando J. Gómez-Ruiz, Stefano Gherardini, Ricardo Puebla

Abstract Understanding the dynamical consequences of quantum phase transitions on thermodynamical quantities, such as work statistics and entropy production, is one of the most intriguing aspect of quantum many-body systems, pinpointing the emergence of irreversibility to critical features. In this work, we investigate the critical fingerprints appearing in these key thermodynamical quantities for a mean-field critical system undergoing a finite-time cycle, starting from a thermal state at a generic inverse temperature. In contrast to non-zero dimensional many-body systems, the presence of a mean-field critical point in a finite-time cycle leads to constant irreversible work even in the limit of infinitely slow driving. This links with the fact that a slow finite-time cycle results in a constant amount of squeezing, which enables us to derive analytical expressions for the work statistics and irreversible entropy, depending solely on the mean-field critical exponents and the functional form of the control parameter near the critical point. We find that the probability of observing negative work values, corresponding to negative irreversible entropy, is inversely proportional to the time the system remains near to the critical point, and this trend becomes less pronounced the lower the temperature of the initial thermal state. Finally, we determine the irreversibility traits under squeezing generation at zero-temperature using the relative entropy of coherence.

Mai Xuan Ly

António M. R. Cadilhe, Vladimir Privman A

We introduce a model with conserved dynamics, where nearest neighbor pairs of spins ↑ ↓ (↓↑) can exchange to assume the configuration ↓ ↑ (↑↓), with rate β (α), through energy decreasing moves only. We report exact solution for the case when one of the rates, α or β, is zero. The irreversibility of such dynamics results in strong dependence on the initial conditions. Domain wall arguments suggest that for more general models with steady states the dynamical critical exponent for the anisotropic spin exchange is different from the isotropic value. – 1

Uwe Krey

T$acirc$nia Tom$eacute$, Alberto Petri

The critical behaviour of two-dimensional stochastic lattice gas models with C 3 v symmetry is analysed. We study the cumulants of the order parameter for the three-state (equilibrium) Potts model and for two irreversible models whose dynamic rules are invariant under the symmetry operations of the point group C 3 v . By means of extensive numerical analysis of the phase transition we show that irreversibility does not affect the critical behaviour of the systems. In particular, we find that the Binder reduced fourth-order cumulant takes a universal value U * which is the same for the three-state Potts model and for the irreversible models. The same universal behaviour is observed for the reduced third-order cumulant.