Quantum Work Distribution Research Articles

Excited-state quantum phase transitions and the entropy of the work distribution in the anharmonic Lipkin-Meshkov-Glick model.

Studying the implications and characterizations of the excited-state quantum phase transitions (ESQPTs) would enable us to understand various phenomena observed in quantum many-body systems. In this work, we delve into the affects and characterizations of the ESQPTs in the anharmonic Lipkin-Meshkov-Glick (LMG) model by means of the entropy of the quantum work distribution. The entropy of the work distribution measures the complexity of the work distribution and behaves as a valuable tool for analyzing nonequilibrium work statistics. We show that the entropy of the work distribution captures salient signatures of the underlying ESQPTs in the model. In particular, a detailed analysis of the scaling behavior of the entropy verifies that it not only acts as a witness of the ESQPTs but also reveals the difference between different types of ESQPTs. We further demonstrate that the work distribution entropy also behaves as a powerful tool for understanding the features and differences of ESQPTs in the energy space. Our results provide further evidence of the usefulness of the entropy of the work distribution for investigating various phase transitions in quantum many-body systems and open up a promising way for experimentally exploring the signatures of ESQPTs.

Exploring quasiprobability approaches to quantum work in the presence of initial coherence: Advantages of the Margenau-Hill distribution.

In quantum thermodynamics, the two-projective-measurement (TPM) scheme provides a successful description of stochastic work only in the absence of initial quantum coherence. Extending the quantum work distribution to quasiprobability is a general way to characterize work fluctuation in the presence of initial coherence. However, among a large number of different definitions, there is no consensus on the most appropriate work quasiprobability. In this article, we list several physically reasonable requirements including the first law of thermodynamics, time-reversal symmetry, positivity of second-order moment, and a support condition for the work distribution. We prove that the only definition that satisfies all these requirements is the Margenau-Hill (MH) quasiprobability of work. In this sense, the MH quasiprobability of work shows its advantages over other definitions. As an illustration, we calculate the MH work distribution of a breathing harmonic oscillator with initial squeezed states and show the convergence to classical work distribution in the classical limit.

Quantum thermodynamics of an Reissner-Nordström black hole

In this paper, we will go beyond equilibrium description to properly investigate the evaporation of a Reissner-Nordström black hole. Thus, we will explicitly apply techniques of non-equilibrium quantum thermodynamics to this black hole. As the non-equilibrium effects would become important at the quantum scale, we will incorporate the quantum gravitational corrections by using an Reissner-Nordström black hole. We will start by developing a novel first law. Then we will investigate the quantum gravitational corrections to the Parikh-Wilczek formalism, and introduce Kullback-Leibler divergence to quantify the effects of corrections. Furthermore, we will demonstrate that the non-thermal nature of radiation in the Parikh-Wilczek formalism can be directly related to the average quantum work done on the emitted particles using non-equilibrium quantum thermodynamics. This is because the average quantum work done is a unitary process in non-equilibrium quantum thermodynamics. We will use the Ramsey scheme for emitted particles to calculate this quantum work distribution for the emitted particles.

The singularities of the rate function of quantum coherent work in one-dimensional transverse field Ising model

Quantum coherence will undoubtedly play a fundamental role in understanding of the dynamics of quantum many-body systems, thereby to reveal its genuine contribution is of great importance. In this paper, we specialize our discussions to the one-dimensional transverse field quantum Ising model initialized in the coherent Gibbs state. After quenching the strength of the transverse field, the effects of quantum coherence are studied by the rate function of quantum work distribution. We find that quantum coherence not only recovers the quantum phase transition destroyed by thermal fluctuations, but also generates some entirely new singularities both in the static state and dynamics. It can be manifested that these singularities are rooted in spin flips causing the sudden change of the domain boundaries of spin polarization. This work sheds new light on the fundamental connection between quantum critical phenomena and quantum coherence.

Entropy of the quantum work distribution

A measure of the complexity of the quantum distribution of work outcomes is presented with general upper and lower bounds in terms of well-known thermodynamic and quantum quantities, thus clearly separating the classical and quantum contributions. This measure is shown to possess a strong signature of the localization phase transition in a quasiperiodic crystal.

Classical theory of universal quantum work distribution in chaotic and disordered non-interacting Fermi systems

We present a universal theory of quantum work statistics in generic disordered non-interacting Fermi systems, displaying a chaotic single-particle spectrum captured by random matrix theory. We consider quantum quenches both within a driven random matrix formalism and in an experimentally accessible microscopic model, describing a two-dimensional disordered quantum dot. By extending Anderson’s orthogonality determinant formula to compute quantum work distribution, we demonstrate that work statistics is non-Gaussian and is characterized by a few dimensionless parameters. At longer times, quantum interference effects become irrelevant and the quantum work distribution is well-described in terms of a purely classical ladder model with a symmetric exclusion process in energy space, while bosonization and mean field methods provide accurate analytical expressions for the work statistics. Our results demonstrate the universality of work distribution in generic chaotic Fermi systems, captured by the analytical predictions of a mean field theory, and can be verified by calorimetric measurements on nanoscale circuits.

Quantum thermodynamics of a quantum sized AdS black hole

In this paper, we investigate the effects of non-perturbative quantum gravitational corrections on a quantum sized AdS black hole. It will be observed that these non-perturbative quantum gravitational corrections modify the stability of this black hole. We will use the non-equilibrium quantum thermodynamics to investigate the evaporation of this black hole between two states. We will analyze the effects of non-perturbative quantum gravitational corrections on this non-equilibrium quantum thermodynamics. We will explicitly obtain the quantum work distribution for this black hole, as it evaporates between two states. It will be observed that this quantum work distribution is modified due to non-perturbative quantum gravitational corrections.

Finite-resolution ancilla-assisted measurements of quantum work distributions

Work is an observable quantity associated with a process; however, there is no Hermitian operator associated with its measurement. We consider an ancilla-assisted protocol measuring the work done on a quantum system driven by a time-dependent Hamiltonian via two von Neumann measurements of the system's energy carried out by a measuring apparatus modeled as a free particle of finite localization and interaction time with the system. We consider system Hamiltonians which both commute and do not commute at different times, finding corrections to fluctuation relations like the Jarzynski equality and the Crooks relation. This measurement model allows us to quantify the effect that measuring has on the estimated work distribution and associated average work done on the system and average heat exchanged with the measuring apparatus.

Thermodynamic uncertainty relation for quantum work distribution: Exact case study for a perturbed oscillator.

Recently, some general relations have been intensively investigated in nonequilibrium mesoscopic systems. In particular, the thermodynamic uncertainty relation (TUR) provides a general bound of the precision for the fluctuation of some currents in terms of the corresponding entropy production. On the other hand, the fluctuation of the work performed is also a significant quantity, which is supposed to satisfy TUR under some conditions, such as symmetric driving protocol. In this paper, we analytically show that the TUR holds for the work performed on an externally perturbed quantum harmonic oscillator interacting with multiple reservoirs in full quantum regime. In this manner, we evaluate how the noncommutativity affects the thermodynamic precision. We also explore its experimental accessibility.

Work-distribution quantumness and irreversibility when crossing a quantum phase transition in finite time

The thermodynamic behavior of out-of-equilibrium quantum systems in finite-time dynamics encompasses the description of energy fluctuations, which dictates a series of system's physical properties. In addition, strong interactions in many-body systems strikingly affect the energy-fluctuation statistics along a non-equilibrium dynamics. By driving transient currents to oppose the precursor to metal-Mott insulator transition in a diversity of dynamical regimes, we show how increasing correlations dramatically affect the statistics of energy fluctuations and consequently the quantum work distribution of finite Hubbard chains. Statistical properties of such distributions, as its skewness, that changes dramatically across the transition, can be related to irreversibility and entropy production. Even close to adiabaticity, the quasi quantum phase transition hinders equilibration, increasing the process irreversibility, and inducing strong quantum features in the quantum work distribution. In the Mott-insulating phase the work fluctuation-dissipation balance gets modified, with the irreversible entropy production dominating over work fluctuations. The effect of an interaction-driven quantum-phase-transition on thermodynamics quantities and irreversibility has to be considered in the design of protocols in small scale devices for application in quantum technology. Eventually, such many-body effects can also be employed in work extraction and refrigeration protocols at quantum scale.

Duality in quantum work

An open question of fundamental importance in quantum thermodynamics is how to describe the statistics of work for the initial state with quantum coherence. In this paper, work statistics is considered from the perspective of ``wave-particle'' duality. Based on the generalized quantum work measurement, predictability of energy levels ${\mathcal{D}}_{W}$ and effectiveness of coherence ${\mathcal{V}}_{W}$ are defined, and they obey inequality ${\mathcal{D}}_{W}^{2}+{\mathcal{V}}_{W}^{2}\ensuremath{\le}1$, which is the fundamental tradeoff relations between the contributions of population and coherence to quantum work distribution. As an application, we consider a driven two-level system and discuss the condition of the bound of above tradeoff relation. These results shed light on the effects of quantum coherence in quantum thermodynamics.

Group-theoretical approach to the calculation of quantum work distribution

Usually the calculation of work distributions in an arbitrary nonequilibrium process in a quantum system, especially in a quantum many-body system is extremely cumbersome. For all quantum systems described by quadratic Hamiltonians, we invent a universal method for solving the work distribution of quantum systems in an arbitrary driving process by utilizing the group-representation theory. This method enables us to efficiently calculate work distributions where previous methods fail. In some specific models, such as the time-dependent harmonic oscillator, the dynamical Casimir effect, and the transverse XY model, the exact and analytical solutions of work distributions in an arbitrary nonequilibrium process are obtained. Our work initiates the study of quantum stochastic thermodynamics based on group-representation theory.

Quantum work distributions associated with the dynamical Casimir effect

We study the joint probability distribution function of the work and the change of photon number of the nonequilibrium process of driving the electromagnetic (EM) field in a three-dimensional cavity with an oscillating boundary. The system is initially prepared in a grand canonical equilibrium state and we obtain the analytical expressions of the characteristic functions of work distributions in the single-resonance and multiple-resonance conditions. Our study demonstrates the validity of the fluctuation theorems of the grand canonical ensemble in nonequilibrium processes with particle creation and annihilation. In addition, our work illustrates that in the high temperature limit, the work done on the quantized EM field approaches its classical counterpart; while in the low temperature limit, similar to Casimir effect, it differs significantly from its classical counterpart.

Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems

Characterizing the work statistics of driven complex quantum systems is generally challenging because of the exponential growth with the system size of the number of transitions involved between different energy levels. We consider the quantum work distribution associated with the driving of chaotic quantum systems described by random matrix Hamiltonians and characterize exactly the work statistics associated with a sudden quench for arbitrary temperature and system size. Knowledge of the work statistics yields the Loschmidt echo dynamics of an entangled state between two copies of the system of interest, the thermofield double state. This echo dynamics is dictated by the spectral form factor. We discuss its relation to frame potentials and its use to assess information scrambling.

Time-reversal symmetric work distributions for closed quantum dynamics in the histories framework

A central topic in the emerging field of quantum thermodynamics is the definition of thermodynamic work in the quantum regime. One widely used solution is to define work for a closed system undergoing non-equilibrium dynamics according to the two-point energy measurement scheme. However, due to the invasive nature of measurement the two-point quantum work probability distribution cannot describe the statistics of energy change from the perspective of the system alone. We here introduce the quantum histories framework as a method to characterise the thermodynamic properties of the unmeasured, closed dynamics. Constructing continuous power operator trajectories allows us to derive an alternative quantum work distribution for closed quantum dynamics that fulfils energy conservation and is time-reversal symmetric. This opens the possibility to compare the measured work with the unmeasured work, contrasting with the classical situation where measurement does not affect the work statistics. We find that the work distribution of the unmeasured dynamics leads to deviations from the classical Jarzynski equality and can have negative values highlighting distinctly non-classical features of quantum work.

Quantum-to-classical transition in the work distribution for chaotic systems.

The work distribution is a fundamental quantity in nonequilibrium thermodynamics mainly due to its connection with fluctuation theorems. Here, we develop a semiclassical approximation to the work distribution for a quench process in chaotic systems that provides a link between the quantum and classical work distributions. The approach is based on the dephasing representation of the quantum Loschmidt echo and on the quantum ergodic conjecture, which states that the Wigner function of a typical eigenstate of a classically chaotic Hamiltonian is equidistributed on the energy shell. Using numerical simulations, we show that our semiclassical approximation accurately describes the quantum distribution as the temperature is increased.

Understanding quantum work in a quantum many-body system.

Based on previous studies in a single-particle system in both the integrable [Jarzynski, Quan, and Rahav, Phys. Rev. X 5, 031038 (2015)2160-330810.1103/PhysRevX.5.031038] and the chaotic systems [Zhu, Gong, Wu, and Quan, Phys. Rev. E 93, 062108 (2016)1539-375510.1103/PhysRevE.93.062108], we study the the correspondence principle between quantum and classical work distributions in a quantum many-body system. Even though the interaction and the indistinguishability of identical particles increase the complexity of the system, we find that for a quantum many-body system the quantum work distribution still converges to its classical counterpart in the semiclassical limit. Our results imply that there exists a correspondence principle between quantum and classical work distributions in an interacting quantum many-body system, especially in the large particle number limit, and further justify the definition of quantum work via two-point energy measurements in quantum many-body systems.

Quantum-classical correspondence principle for work distributions in a chaotic system.

We numerically study the work distributions in a chaotic system and examine the relationship between quantum work and classical work. Our numerical results suggest that there exists a correspondence principle between quantum and classical work distributions in a chaotic system. This correspondence was proved for one-dimensional integrable systems in a recent work [Jarzynski, Quan, and Rahav, Phys. Rev. X 5, 031038 (2015)1063-651X10.1103/PhysRevX.5.031038]. Our investigation further justifies the definition of quantum work via two-point energy measurements.

Quantum work statistics of charged Dirac particles in time-dependent fields.

The quantum Jarzynski equality is an important theorem of modern quantum thermodynamics. We show that the Jarzynski equality readily generalizes to relativistic quantum mechanics described by the Dirac equation. After establishing the conceptual framework we solve a pedagogical, yet experimentally relevant, system analytically. As a main result we obtain the exact quantum work distributions for charged particles traveling through a time-dependent vector potential evolving under Schrödinger as well as under Dirac dynamics, and for which the Jarzynski equality is verified. Special emphasis is put on the conceptual and technical subtleties arising from relativistic quantum mechanics.

Quantum-Classical Correspondence Principle for Work Distributions

The definition of quantum work differs markedly from the definition found in classical mechanics textbooks. Now, by showing that quantum work distributions can be understood as interference patterns between classical trajectories, researchers bridge the gap between classical and quantum notions of work.