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arXiv:2004.01126 · Physical Review Research

Wehrl entropy production rate across a dynamical quantum phase transition

Bruno O. Goes, G. T. Landi, E. Solano, M. Sanz, Lucas C. Céleri

Published Sep 15, 2020• 22 citations
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Abstract

This paper proposes the Husimi-Q function based entropy as a suitable quantity to describe the thermodynamic properties of dynamical phase transitions, and establishes a relation between dynamical criticality and entropy production.
DOI
10.1103/physrevresearch.2.033419

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This research demonstrates that entropy-based measures, calculated from marginals of the Husimi functions, effectively identify and characterize quantum phase transitions in the Lipkin-Meshkov-Glick model. The study reveals that changes in entropy, particularly Wehrl entropy, marginal entropies, and mutual information, act as sensitive indicators of criticality, distinguishing between different transition orders and highlighting the breakdown of separability near critical points. These findings establish entropy analysis as a powerful, complementary tool to traditional methods for understanding quantum criticality in many-body systems.
The thermodynamics of quantum phase transitions has long been a rich area of research, providing numerous insights and enhancing our understanding of this important phenomenon. This theoretical framework has been well developed specially because quantum phase transitions occur at equilibrium. However, its dynamical counterpart, known as dynamical quantum phase transitions, takes place out of equilibrium, where conventional thermodynamic tools are inapplicable. In this work we make progress in this area by connecting dynamical criticality to thermodynamics through a geometric perspective on entropy production. Our findings, along with other recent developments, suggest that dynamical criticality can lead the system to highly complex dynamics, indicating a possible pathway to thermalization.
We propose a broadly applicable formalism for the description of coarse grained en-tropy production in quantum mechanical processes. Our formalism is based on the Husimi transform of the quantum state, which encodes the notion that information about any quan-tum state is limited by the experimental resolution. We show in two analytically tractable cases (the decay of an unstable vacuum state and reheating after cosmic inflation) that the growth rate of the Wehrl entropy associated with the Husimi function approaches the classi-cal Kolmogorov-Sinäı entropy. We also discuss various possible applications of our formalism, including the production of entropy in the early stages of a relativistic heavy ion collision. The production of entropy at the quantum level, i. e. the loss of information about the state of the system under consideration, is a long-standing problem in statistical physics. Many of its conceptual aspects are similar to those encountered in classical physics, but quantum mechanics poses the additional, but closely related,
Symmetries play a central role in both equilibrium and nonequilibrium phase transitions, yet their quantitative characterization in dynamical quantum phase transitions (DQPTs) remains an open challenge. In this work, we establish a direct connection between symmetry properties of a many-body model and measures of quantum asymmetry, showing that asymmetry monotones provide a robust and physically transparent indicator of dynamical quantum criticality. Focusing on the quenched Lipkin-Meshkov-Glick model, we demonstrate that asymmetry measures associated with collective spin generators faithfully capture the onset of DQPTs, reflecting the dynamical restoration or breaking of underlying symmetries. Remarkably, the time-averaged asymmetry exhibits clear signatures of the dynamical critical point, in close correspondence with both the dynamical order parameter and the behavior of entropy production. We further uncover a quantitative link between asymmetry generation and thermodynamic irreversibility, showing that peaks in asymmetry coincide with maximal entropy production across the transition. Our results position asymmetry as a unifying concept bridging symmetry, information-theoretic quantifiers, and nonequilibrium thermodynamics in dynamical quantum phase transitions, providing a powerful framework for understanding critical dynamics beyond traditional order parameters.
Phase transitions represent fundamental transformations of matter, characterized by abrupt changes in macroscopic properties and often associated with singular behavior at critical points. While equilibrium aspects of phase transitions, particularly universal critical exponents and scaling laws, are well-understood, the non-equilibrium processes occurring near criticality, especially the production of entropy, remain a rich area of investigation. This paper explores the intricate relationship between critical entropy production and the emergence of scaling laws in systems undergoing phase transitions. We delve into how the rate of entropy production diverges or exhibits anomalous scaling near critical points, reflecting the system's attempts to dissipate energy and respond to external perturbations as it approaches a state of macroscopic change. By integrating concepts from non-equilibrium thermodynamics, statistical mechanics, and renormalization group theory, we aim to elucidate the underlying mechanisms that govern entropy generation in these critical regimes. We discuss theoretical frameworks that predict universal scaling behaviors for entropy production rates, analogous to those observed for equilibrium order parameters and susceptibilities. The implications of these scaling laws extend beyond theoretical physics, offering insights into complex systems, far-from-equilibrium dynamics, and the efficiency of energy conversion processes in critical environments. Our analysis highlights the critical entropy production as a unique signature of non-equilibrium dynamics during phase transitions, providing a deeper understanding of the interplay between fluctuations, dissipation, and universality near points of instability.