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.

14 pages, 9 figures

References in corpus (9)

• Novel type of phase transition in a system of self-driven particles
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Work and information processing in a solvable model of Maxwell's demon
• Efficiency of cellular information processing
• Absence of First-order Transition and Tri-critical Point in the Dynamic Phase Diagram of a Spatially Extended Bistable System in an Oscillating Field
• Directed flow in non-adiabatic stochastic pumps
• The unified geometric theory of mesoscopic stochastic pumps and reversible ratchets
• Stochastic thermodynamics with information reservoirs
• Dynamic phase transition in the two-dimensional kinetic Ising model in an oscillating field: Universality with respect to the stochastic dynamic

Cited by in corpus (18)

• Irreversible entropy production, from quantum to classical
• A unifying framework for mean-field theories of asymmetric kinetic Ising systems
• Thermodynamics and computation during collective motion near criticality
• Entropy production at criticality in a nonequilibrium Potts model
• Nonequilibrium thermodynamics of the asymmetric Sherrington-Kirkpatrick model
• Exponential volume dependence of entropy-current fluctuations at first-order phase transitions in chemical reaction networks
• Diverging current fluctuations in critical Kerr resonators
• Quantum features of entropy production in driven-dissipative transitions
• Multicritical dissipative phase transitions in the anisotropic open quantum Rabi model
• Current fluctuations in nonequilibrium discontinuous phase transitions
• Precision and dissipation of a stochastic Turing pattern
• Heat current and entropy production rate in local non-Markovian quantum dynamics of global Markovian evolution
• Nonequilibrium fluctuations of chemical reaction networks at criticality: The Schlögl model as paradigmatic case
• Thermodynamics of Encoding and Encoders
• Inferring the Langevin Equation with Uncertainty via Bayesian Neural Networks
• Thermodynamics of Darwinian selection in molecular replicators
• Multiparty Spohn's theorem for a combination of local Markovian and non-Markovian quantum dynamics
• Typical Positivity of Nonequilibrium Entropy Production for Pure States