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

TL;DR

This paper investigates the critical behavior of entropy production in the Ising model under oscillating magnetic fields, revealing different phase transition signatures in mean-field and two-dimensional cases, and explores the system's learning rate as an information sensor.

Contribution

It demonstrates how entropy production behaves at phase transitions in the Ising model with oscillating fields and introduces a model linking the system's learning rate to critical phenomena.

Findings

Entropy production rate shows discontinuity at first-order transitions.

In 2D, entropy production's first derivative diverges logarithmically at criticality.

The system's learning rate exhibits a jump at the critical point.

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.