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Quantum coherence and criticality in irreversible work

Adalberto D. Varizi, André P. Vieira, Cormick, Maria Cecilia, Raphael C. Drumond, Gabriel Teixeira Landi

Published Aug 1, 2020• 23 citations
OpenAlex

Abstract

The irreversible work during a driving protocol constitutes one of the most widely studied measures in nonequilibrium thermodynamics, as it constitutes a proxy for entropy production. In quantum systems, it has been shown that the irreversible work has an additional, genuinely quantum mechanical contribution, due to coherence produced by the driving protocol. The goal of this paper is to explore this contribution in systems that undergo a quantum phase transition. Substantial effort has been dedicated in recent years to understanding the role of quantum criticality in work protocols. However, practically nothing is known about how coherence contributes to it. To shed light on this issue, we study the entropy production in infinitesimal quenches of the one-dimensional XY model. We find that coherence plays a significant role in the entropy production and can even account for most of it in certain situations. Moreover, at low temperatures, the coherence presents a finite cusp at the critical point, whereas the entropy production diverges logarithmically. For high temperatures, however, the coherence presents a kink at the critical point indicating the quantum phase transition that occurs only at T=0. Alternatively, if the quench is performed in the anisotropy parameter, then we find that there are situations where all of the entropy produced is due to quantum coherences.

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The irreversible work during a driving protocol constitutes one of the most widely studied measures in nonequilibrium thermodynamics, as it constitutes a proxy for entropy production. In quantum systems, it has been shown that the irreversible work has an additional, genuinely quantum mechanical contribution, due to coherence produced by the driving protocol. The goal of this paper is to explore this contribution in systems that undergo a quantum phase transition. Substantial effort has been dedicated in recent years to understanding the role of quantum criticality in work protocols. However, practically nothing is known about how coherence contributes to it. To shed light on this issue, we study the entropy production in infinitesimal quenches of the one-dimensional XY model. We find that coherence plays a significant role in the entropy production and can even account for most of it in certain situations. Moreover, at low temperatures, the coherence presents a finite cusp at the critical point, whereas the entropy production diverges logarithmically. For high temperatures, however, the coherence presents a kink at the critical point indicating the quantum phase transition that occurs only at T=0. Alternatively, if the quench is performed in the anisotropy parameter, then we find that there are situations where all of the entropy produced is due to quantum coherences.
The entropy produced when a system undergoes an infinitesimal quench is directly linked to the work parameter susceptibility, making it sensitive to the existence of a quantum critical point. Its singular behavior at T=0T=0T=0, however, disappears as the temperature is raised, hindering its use as a tool for spotting quantum phase transitions. Notwithstanding, the entropy production can be split into classical and quantum components, related with changes in populations and coherences. In this paper we show that these individual contributions can continue to exhibit signatures of the quantum phase transition, even at arbitrarily high temperatures. This is a consequence of their intrinsic connection to the derivatives of the energy eigenvalues and the energy eigenbasis. We illustrate our results in the Landau-Zener model and the prototypical quantum critical system, the XYXYXY model.
Abstract The entropy produced when a quantum system at thermal equilibrium is driven to a non-equilibrium state can be considered as having components from coherence generation and from a population mismatch. The entropy component which is related to coherence represents a truly quantum effect and can be calculated using two different decompositions, based on either the relative entropy of coherence or on the thermal state corresponding to the Hamiltonian dephased in the eigen basis of the actual state. However, the decomposition based on the relative entropy was unable to quantify highly coherent processes or processes occurring in the low temperature regime. We experimentally explored a general driving scheme (a non-equilibrium process) on a nuclear magnetic resonance quantum processor, and were able to isolate the contribution of coherence to irreversible entropy generation. Furthermore, we numerically explored an infinitesimal driving process to distinguish between high and low temperature limits. The thermal equilibrium temperature and the final energy gap were varied to establish the relationship among temperature, energy level spacing, entropy production and coherence generation. Our results indicate that the contribution to entropy from coherence is higher in the low temperature regime. We also verified a generalized Clausius inequality, which affirms that the irreversible entropy production is lower-bounded.
The emerging field of quantum thermodynamics is contributing important results and insights into archetypal many-body problems, including quantum phase transitions. Still, the question whether out-of-equilibrium quantities, such as fluctuations of work, exhibit critical scaling after a sudden quench in a closed system has remained elusive. Here, we take a novel approach to the problem by studying a quench across an impurity quantum critical point. By performing density matrix renormalization group computations on the two-impurity Kondo model, we are able to establish that the irreversible work produced in a quench exhibits finite-size scaling at quantum criticality. This scaling faithfully predicts the equilibrium critical exponents for the crossover length and the order parameter of the model, and, moreover, implies an exponent for the rescaled irreversible work. By connecting the irreversible work to the two-impurity spin correlation function, our findings can be tested experimentally.
Abstract Thermodynamic irreversibility is well characterized by the entropy production arising from non-equilibrium quantum processes. We show that the entropy production of a quantum system undergoing open-system dynamics can be formally split into a term that only depends on population unbalances, and one that is underpinned by quantum coherences. This allows us to identify a genuine quantum contribution to the entropy production in non-equilibrium quantum processes. We discuss how these features emerge both in Lindblad-Davies differential maps and finite maps subject to the constraints of thermal operations. We also show how this separation naturally leads to two independent entropic conservation laws for the global system-environment dynamics, one referring to the redistribution of populations between system and environment and the other describing how the coherence initially present in the system is distributed into local coherences in the environment and non-local coherences in the system-environment state. Finally, we discuss how the processing of quantum coherences and the incompatibility of non-commuting measurements leads to fundamental limitations in the description of quantum trajectories and fluctuation theorems.
Driven-dissipative phase transitions are currently a topic of intense research due to the prospect of experimental realizations in quantum optical setups. The most paradigmatic model presenting such a transition is the Kerr model, which predicts the phenomenon of optical bistability, where the system may relax to two different steady states for the same driving condition. These states, however, are inherently out-of-equilibrium and are thus characterized by the continuous production of irreversible entropy, a key quantifier in thermodynamics. In this paper, we study the dynamics of the entropy production rate in a quench scenario of the Kerr model, where the external pump is abruptly changed. This is accomplished using a recently developed formalism, based on the Husimi QQQ-function, which is particularly tailored for driven-dissipative and non-Gaussian bosonic systems, Goes et al. [Phys. Rev. Res. 2, 013136 (2020)]. Within this framework, the entropy production can be split into two contributions, one being extensive with the drive and describing classical irreversibility, and the other being intensive and directly related to quantum fluctuations. The latter, in particular, is found to reveal the high degree of nonadiabaticity for quenches between different metastable states.