Work Fluctuations Research Articles

Shortcut-to-adiabaticity Otto engine: A twist to finite-time thermodynamics.

We consider a finite-time Otto engine operating on a quantum harmonic oscillator and driven by shortcut-to-adiabaticity (STA) techniques to speed up its cycle. We study its efficiency and power when internal friction, time-averaged work, and work fluctuations are used as quantitative figures of merit, showing that time-averaged efficiency and power are useful cost functions for the characterization of the performance of the engine. We then use the minimum allowed time for validity of STA protocol relation to establish a physically relevant bound to the efficiency at maximum power of the STA-driven cycle.

Scaling properties of work fluctuations after quenches near quantum transitions

We study the scaling properties of the statistics of the work done on a generic many-body system at a quantum phase transition of any order and type, arising from quenches of a driving control parameter. For this purpose we exploit a dynamic finite-size scaling framework. Namely, we put forward the existence of a nontrivial finite-size scaling limit for the work distribution, defined as the large-size limit when appropriate scaling variables are kept fixed. The corresponding scaling behaviors are thoroughly verified by means of analytical and numerical calculations in two paradigmatic many-body systems as the quantum Ising model and the Bose–Hubbard model.

Effects of multisite interaction on nonequilibrium thermodynamics of XY spin chain in a transverse filed

In recent years, the property of nonequilibrium thermodynamics in closed system, especially in spin chain system undergoing a quenching process, has become one of the hot topics in the quantum thermodynamics. The nonequilibrium thermodynamic properties of XY spin chain with XZX + YZY type of three-site interaction under a transverse field are studied by considering an exactly solvable model. First we review some basic concepts, i.e., the work distribution, the averaged work, the fluctuation of work, and the irreversible entropy in the nonequilibrium thermodynamics, and give the theoretical model and its solutions. Then, we concretely discuss the effects of the three-site interaction of XZX + YZY type on the average work, the fluctuation of work and the irreversible entropy in the extended XY chain undergoing a quench process. The theoretical calculation and numerical simulation show that the three-site interaction of XZX + YZY type may play a positive and negative role in the increase of the averaged work, which depends on the strength of initial external magnetic field. Moreover, we also find that work fluctuation can be effectively suppressed by adjusting the intensity of XZX + YZY three-site interaction. Finally, it is found that the irreversible entropy production presents a sharp peak characteristic near the critical magnetic field, and the value of the peak sharp decreases with the increase of XZX + YZY three-site interaction. Simultaneously, the corresponding physical explanations are also given. In a word, the results given in present paper may increasingly arouse one’s interest in the nonequilibrium quantum thermodynamics.

Conservation laws and work fluctuation relations in chemical reaction networks.

We formulate a nonequilibrium thermodynamic description for open chemical reaction networks (CRNs) described by a chemical master equation. The topological properties of the CRN and its conservation laws are shown to play a crucial role. They are used to decompose the entropy production into a potential change and two work contributions, the first due to time dependent changes in the externally controlled chemostats concentrations and the second due to flows maintained across the system by nonconservative forces. These two works jointly satisfy a Jarzynski and Crooks fluctuation theorem. In the absence of work, the potential is minimized by the dynamics as the system relaxes to equilibrium and its equilibrium value coincides with the maximum entropy principle. A generalized Landauer's principle also holds: the minimal work needed to create a nonequilibrium state is the relative entropy of that state to its equilibrium value reached in the absence of any work.

Fluctuation-theorem method of measuring a particle's mass without knowing its shape or density

Tracking the Brownian motion of aerosol particles as they settle in air allows a mass measurement. The particle typically falls downward at its terminal settling velocity; however, the particle occasionally will be displaced upwards due to Brownian fluctuations. The number of occurrences of upward and downward fluctuations is compared, using the formula for the work fluctuation theorem, to yield the mass. This method can be applied to either a single particle or a collection of particles. The advantages of this method include no required information about the size, shape, or density of the particle. Details of the analysis method are presented and illustrated with experimental data.

An autonomous quantum machine to measure the thermodynamic arrow of time

According to the second law of thermodynamics, the evolution of physical systems has a preferred direction, that is characterized by some positive entropy production. Here we propose a direct way to measure the stochastic entropy produced while driving a quantum open system out of thermal equilibrium. The driving work is provided by a quantum battery, the system and the battery forming an autonomous machine. We show that the battery’s energy fluctuations equal work fluctuations and check Jarzynski’s equality. As these energy fluctuations are measurable, the battery behaves as an embedded quantum work meter and the machine verifies a generalized fluctuation theorem involving the information encoded in the battery. Our proposal can be implemented with state-of-the-art opto-mechanical systems. It paves the way toward the experimental demonstration of fluctuation theorems in quantum open systems.

Transient and thermo-economic analysis of MED-MVC desalination system

An exergo-economic model is used to assess the performance of a multi-effect desalination plant integrated to a mechanical vapor compressor unit (MED-MVC) with a water production capacity of 1500 m3/day. The results show that the second law efficiency (ηII) is 2.8%. The MVC and evaporator units are responsible for about 39 and 52% of the total exergy destruction, respectively. The total water price (TWP) is 1.70 $/m3 when calculated using a simple conventional economic model and 1.63 $/m3 when calculated using an exergy-based cost model. Increasing the number of effects from 1 to 6 results in a 39% reduction in the specific power consumption (SPC), a 70% increase in ηII and a 24% decrease in TWP. A dynamic model is developed to investigate the effect of fluctuations of compressor work (W˙c) and inlet seawater temperature (Tsw) on the plant behavior and performance. The dynamic model results show that the disturbance in W˙c has a significant effect on the plant transient behavior and may cause the plant to cease operation while a disturbance in Tsw has only a moderate impact. Increasing Tsw above a certain value of the steady-state condition without proper control on the plant response could lead to evaporator dry out. In term of performance, a reduction in W˙c causes a decrease in the plant production capacity and SPC, while it increases the plant performance ratio (PR). On the other hand, a reduction in the inlet Tsw causes a reduction in the plant production capacity and PR and an increase in SPC for the same compressor work. Furthermore, a comparison between a MED-MVC system and a MED integrated to a thermal vapor compressor system (MED-TVC) reveals that the latter system is rather sensitive to the reduction in Tsw due to the presence of the condenser unit in the MED-TVC. The response of the MED-MVC system is slower than the MED-TVC which is due to the high thermal capacity of the preheaters for the feed in the MED-MVC.

Work fluctuation and its optimal extraction with time dependent harmonic potential from a non-Markovian bath

We study the optimal work extraction protocol for a Brownian particle described by generalized Langevin dynamics from a single reservoir with the aid of position measurement. The particle is confined in a time dependent harmonic potential. In the overdamped situation, we show that memory effects typically reduce the extracted work, and full information-work conversion can only be achieved by manipulating both the stiffness and center of the potential quasistatically. In the non-Markovian underdamped regime, we investigate the exponential tail of work distribution using the path integral formalism, memory effects on the characteristic work production is also revealed.

Measurement-driven single temperature engine

A four stroke quantum engine which alternately interacts with a measurement apparatus and a single heat bath is discussed in detail with respect to the average work and heat as well as to the fluctuations of work and heat. The efficiency and the reliability of such an engine with a harmonic oscillator as working substance are analyzed under different conditions such as different speeds of the work strokes, different temperatures of the heat bath and various strengths of the energy supplying measurement. For imperfect thermalization strokes of finite duration also the power of the engine is analyzed. A comparison with a two-temperature Otto engine is provided in the particular case of adiabatic work and ideal thermalization strokes.

Hidden entropy production and work fluctuations in an ideal active gas.

Collections of self-propelled particles that move persistently by continuously consuming free energy are a paradigmatic example of active matter. In these systems, unlike Brownian "hot colloids," the breakdown of detailed balance yields a continuous production of entropy at steady state, even for an ideal active gas. We quantify the irreversibility for a noninteracting active particle in two dimensions by treating both conjugated and time-reversed dynamics. By starting with underdamped dynamics, we identify a hidden rate of entropy production required to maintain persistence and prevent the rapidly relaxing momenta from thermalizing, even in the limit of very large friction. Additionally, comparing two popular models of self-propulsion with identical dissipation on average, we find that the fluctuations and large deviations in work done are markedly different, providing thermodynamic insight into the varying extents to which macroscopically similar active matter systems may depart from equilibrium.

Critical slowing down of multiatom entanglement by Rydberg blockade

Laser excitation pulses that lead to perfect adiabatic state transfer in an ensemble of three-level ladder atoms lead to highly entangled states of many atoms if their highest excited state is subject to Rydberg blockade. Solution of the Schr\"odinger equation shows that it is increasingly difficult to ensure the adiabatic evolution as the number of atoms increases. A diminishing energy gap, significant variations in collective observables, and increased work fluctuations link the critical slowing down of the adiabatic evolution with a quantum phase transition-like behavior of the system.

Experimental demonstration of work fluctuations along a shortcut to adiabaticity with a superconducting Xmon qubit

In a ‘shortcut to adiabaticity’ (STA) protocol, the counter-diabatic Hamiltonian, which suppresses the non-adiabatic transition of a reference ‘adiabatic’ trajectory, induces a quantum uncertainty of the work cost in the framework of quantum thermodynamics. Following a theory derived recently (Funo et al 2017 Phys. Rev. Lett. 118 100602), we perform an experimental measurement of the STA work statistics in a high-quality superconducting Xmon qubit. Through the frozen-Hamiltonian and frozen-population techniques, we experimentally realize the two-point measurement of the work distribution for given initial eigenstates. Our experimental statistics verify (i) the conservation of the average STA work and (ii) the equality between the STA excess of work fluctuations and the quantum geometric tensor.

Entropy production and work fluctuation relations for a single particle in active bath

A colloidal particle immersed in a bath of bacteria is a typical example of a passive particle in an active bath. To model this, we take an overdamped harmonically trapped particle subjected to a thermal and a non-equilibrium noise arising from the active bath. The harmonic well can be attributed to a laser trap or to the small amplitude motion of the sedimented colloid at the bottom of the capillary. In the long time, the system reaches a non-equilibrium steady state that can be described by an effective temperature. Here we investigate whether fluctuation relations for entropy hold in the presence of Gaussian active noise. In addition, when subjected to a deterministic time dependent drag, we find that transient fluctuation theorem for work cannot be applied in conventional form. However, a steady state fluctuation relation for work emerges out with a renormalized temperature.

A generalized linear response framework for expanded ensemble and replica exchange simulations.

Expanded ensemble simulation is a powerful technique for enhancing sampling over a range of thermodynamic parameters. However, although the premise is relatively simple, running successful simulations in practice still presents something of an ad hoc challenge. Three main difficulties exist: (1) the selection of the thermodynamic states, (2) the selection of the sampling weights, and (3) efficient sampling of the expanded parameter space. Here we consider these problems in the context of a pairwise linear response approach to the work fluctuation theorem. The approach offers comprehensive tactics for addressing the three difficulties and can be used as either an alternative or a complement to replica exchange simulations. Importantly, the results are trivially implemented for multi-dimensional parameter spaces and they recover results from the literature aimed at the special cases of simulated/parallel tempering and replica exchange umbrella sampling. Illustrative examples are shown using the NAMD simulation engine.

Thermodynamic work statistics for Ornstein–Uhlenbeck-type heat baths

In this work we explore the validity of the transient work fluctuation theorem as well as the Jarzynski equality. In the case of a Brownian particle dragged through a fluid by an optical trap, the fluid plays the role of a non-Markovian heat bath characterized by an specific Ornstein–Uhlenbeck friction memory kernel. To achieve our goal, we used an alternative method which transformed the generalized Langevin equation into an equivalent third-order non-Markovian Langevin equation. By means of the exact analytical solution of this Langevin equation, we calculated the statistics of thermodynamic work which established the Crooks relation, and then the Jarzynski equality came immediately. The fluctuation theorems are applicable to small systems where energy fluctuations with respect to the average behavior are big enough to be measured. The examples of such a class of systems are found inside living organisms.

Effects of quantum coherence on work statistics

In the conventional two-point measurement scheme of quantum thermodynamics, quantum coherence is destroyed by the first measurement. But as we know the coherence really plays an important role in the quantum thermodynamics process, and how to describe the work statistics for a quantum coherent process is still an open question. In this paper, we use the full counting statistics method to investigate the effects of quantum coherence on work statistics. First, we give a general discussion and show that for a quantum coherent process, work statistics is very different from that of the two-point measurement scheme, specifically the average work is increased or decreased and the work fluctuation can be decreased by quantum coherence, which strongly depends on the relative phase, the energy level structure and the external protocol. Then, we concretely consider a quenched 1-D transverse Ising model, and show that quantum coherence has a more significant influence on work statistics in the ferromagnetism regime compared with that in the paramagnetism regime, so that due to the presence of quantum coherence the work statistics can exhibit the critical phenonmenon even at high temperature.

Experimental demonstration that a free-falling aerosol particle obeys a fluctuation theorem.

We investigate the fluctuating motion of an aerosol particle falling in air. Using a Millikan-like setup, we tracked a 1-μm sphere falling at its terminal velocity. We observe occurrences of particles undergoing upward displacements against the force of gravity, so that negative work is done briefly. These negative-work events have a probability that is shown to obey the work fluctuation theorem. This experimental confirmation of the theorem's applicability to aerosols leads us to develop and demonstrate an application: an in situ measurement of an aerosol particle's mass.

Phase Transition in Protocols Minimizing Work Fluctuations.

For two canonical examples of driven mesoscopic systems-a harmonically trapped Brownian particle and a quantum dot-we numerically determine the finite-time protocols that optimize the compromise between the standard deviation and the mean of the dissipated work. In the case of the oscillator, we observe a collection of protocols that smoothly trade off between average work and its fluctuations. However, for the quantum dot, we find that as we shift the weight of our optimization objective from average work to work standard deviation, there is an analog of a first-order phase transition in protocol space: two distinct protocols exchange global optimality with mixed protocols akin to phase coexistence. As a result, the two types of protocols possess qualitatively different properties and remain distinct even in the infinite duration limit: optimal-work-fluctuation protocols never coalesce with the minimal-work protocols, which therefore never become quasistatic.

Precision and Work Fluctuations in Gaussian Battery Charging

One of the most fundamental tasks in quantum thermodynamics is extracting energy from one system and subsequently storing this energy in an appropriate battery. Both of these steps, work extraction and charging, can be viewed as cyclic Hamiltonian processes acting on individual quantum systems. Interestingly, so-called passive states exist, whose energy cannot be lowered by unitary operations, but it is safe to assume that the energy of any not fully charged battery may be increased unitarily. However, unitaries raising the average energy by the same amount may differ in qualities such as their precision, fluctuations, and charging power. Moreover, some unitaries may be extremely difficult to realize in practice. It is hence of crucial importance to understand the qualities that can be expected from practically implementable transformations. Here, we consider the limitations on charging batteries when restricting to the feasibly realizable family of Gaussian unitaries. We derive optimal protocols for general unitary operations as well as for the restriction to easier implementable Gaussian unitaries. We find that practical Gaussian battery charging, while performing significantly less well than is possible in principle, still offers asymptotically vanishing relative charge variances and fluctuations.

Work probability distribution for a ferromagnet with long-ranged and short-ranged correlations.

Work fluctuations and work probability distributions are fundamentally different in systems with short-ranged versus long-ranged correlations. Specifically, in systems with long-ranged correlations the work distribution is extraordinarily broad compared to systems with short-ranged correlations. This difference profoundly affects the possible applicability of fluctuation theorems like the Jarzynski fluctuation theorem. The Heisenberg ferromagnet, well below its Curie temperature, is a system with long-ranged correlations in very low magnetic fields due to the presence of Goldstone modes. As the magnetic field is increased the correlations gradually become short ranged. Hence, such a ferromagnet is an ideal system for elucidating the changes of the work probability distribution as one goes from a domain with long-ranged correlations to a domain with short-ranged correlations by tuning the magnetic field. A quantitative analysis of this crossover behavior of the work probability distribution and the associated fluctuations is presented.