Critical behavior of entropy production and learning rate: Ising model with an oscillating field

Abstract

We study the critical behavior of the entropy production of the Ising model subject to a magnetic field that oscillates in time. The mean-field model displays a phase transition that can be either first or second-order, depending on the amplitude of the field and on the frequency of oscillation. Within this approximation the entropy production rate is shown to have a discontinuity when the transition is first-order and to be continuous, with a jump in its first derivative, if the transition is second-order. In two dimensions, we find with numerical simulations that the critical behavior of the entropy production rate is the same, independent of the frequency and amplitude of the field. Its first derivative has a logarithmic divergence at the critical point. This result is in agreement with the lack of a first-order phase transition in two dimensions. We analyze a model with a field that changes at stochastic time-intervals between two values. This model allows for an informational theoretic interpretation, with the system as a sensor that follows the external field. We calculate numerically a lower bound on the learning rate, which quantifies how much information the system obtains about the field. Its first derivative with respect to temperature is found to have a jump at the critical point.

Quantum features of entropy production in driven-dissipative transitions

“…They showed that the entropy production rate was always finite, but had a kink at the critical point, with its derivative presenting a logarithmic divergence. A similar behavior was also observed in a Brownian system undergoing an order-disorder transition [47], the majority vote model [48] and a 2D Ising model subject to an oscillating field [49]. In the system of Ref.…”

“…Once again, the unitary part Π u of the entropy production ( Figs. 3(a) and (b)) is found to behave like the mean-field predictions for classical transitions [46][47][48][49][50][51][52]. It is continuous and finite, but presents a kink (the first derivative is discontinuous) at the critical point λ c = ω 0 (κ 2 + ω 2 )/ω.…”

“…The critical behavior in the thermodynamic limit (N → ∞) can be better understood by performing a finite size analysis (Figs. 2(c) and (d)), where we plot Π u and Π d /N vs. N( / c − 1) for multiple values of N. Surprisingly, we find that the behavior of Π u matches exactly that of the classical entropy production in a discontinuous transition [49,51,52] (see [62] for more information). We also see from Fig.…”

Stochastic thermodynamics of all-to-all interacting many-body systems

“…However, little is known about their thermodynamic description. For instance, thermodynamics of nonequilibrium phase transitions started to be explored only recently [18][19][20][21][22][23][24][25][26][27][28][29][30]. There is a pressing need to develop methodologies to study thermodynamic quantities such as heat work and dissipation, not only at the average but also at the fluctuation level.…”

Universality in driven Potts models

“…While the thermodynamics of equilibrium phase transitions in interacting systems has a long history and is well-documented [1,2], it is only as of recent that the thermodynamics of nonequilibrium phase transitions started to be explored [3][4][5][6][7][8][9]. This delay can be attributed to the lack of a theory that systematically describes the thermodynamics of out-of-equilibrium processes.…”