Work Fluctuations Research Articles

Power fluctuations in a finite-time quantum Carnot engine

Stability is an important property of small thermal machines with fluctuating power output. We here consider a finite-time quantum Carnot engine based on a degenerate multilevel system and study the influence of its finite Hilbert space structure on its stability. We optimize in particular its relative work fluctuations with respect to level degeneracy and level number. We find that its optimal performance may surpass those of nondegenerate two-level engines or harmonic oscillator motors. Our results show how to realize high-performance, high-stability cyclic quantum heat engines.Received 13 July 2020Accepted 13 July 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.L032041Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum thermodynamicsStatistical Physics

Comment on "Fluctuations in Extractable Work Bound the Charging Power of Quantum Batteries".

In the abstract of [Phys. Rev. Lett. 125, 040601 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.040601] one can read that "[…] to have a nonzero rate of change of the extractable work, the state ρ_{W} of the battery cannot be an eigenstate of a 'free energy operator,' defined by F≡H_{W}+β^{-1}log(ρ_{W}), where H_{W} is the Hamiltonian of the battery and β is the inverse temperature […]." Contrarily to what is presented below Eq.(17) of the Letter, we observe that the above conclusion does not hold when the battery is subject to nonunitary dynamics.

Bounds on fluctuations for finite-time quantum Otto cycle.

For quantum Otto engine driven quasistatically, we provide exact full statistics of heat and work for a class of working fluids that follow a scale-invariant energy eigenspectra under driving. Equipped with the full statistics we go on to derive a universal expression for the ratio of nth cumulant of output work and input heat in terms of the mean Otto efficiency. Furthermore, for nonadiabatic driving of quantum Otto engine with working fluid consisting of either a (i) qubit or (ii) a harmonic oscillator, we show that the relative fluctuation of output work is always greater than the corresponding relative fluctuation of input heat absorbed from the hot bath. As a result, the ratio between the work fluctuation and the input heat fluctuation receives a lower bound in terms of the square value of the average efficiency of the engine. The saturation of the lower bound is received in the quasistatic limit of the engine.

Jarzynski equality and Crooks relation for local models of air–sea interaction

Abstract. We show that the most prominent of the work theorems, the Jarzynski equality and the Crooks relation, can be applied to the momentum transfer at the air–sea interface using a hierarchy of local models. In the more idealized models, with and without a Coriolis force, the variability is provided from Gaussian white noise which modifies the shear between the atmosphere and the ocean. The dynamics is Gaussian, and the Jarzynski equality and Crooks relation can be obtained analytically solving stochastic differential equations. The more involved model consists of interacting atmospheric and oceanic boundary layers, where only the dependence on the vertical direction is resolved, the turbulence is modeled through standard turbulent models and the stochasticity comes from a randomized drag coefficient. It is integrated numerically and can give rise to a non-Gaussian dynamics. Also in this case the Jarzynski equality allows for calculating a dynamic beta βD of the turbulent fluctuations (the equivalent of the thermodynamic beta β=(kBT)-1 in thermal fluctuations). The Crooks relation gives the βD as a function of the magnitude of the work fluctuations. It is well defined (constant) in the Gaussian models and can show a slight variation in the more involved models. This demonstrates that recent concepts of stochastic thermodynamics used to study micro-systems subject to thermal fluctuations can further the understanding of geophysical fluid dynamics with turbulent fluctuations.

Феноменологическая философия литературы Р. Ингардена. Статус эстетических объектов и их отношение к реальности

The study aims to find out what the basis of any literary work is and what role the reader plays in formation of the image of this type of art in the process of its perception. R. Ingarden’s understanding of the literary work is that of a purely intentional object, so there emerges the issue of its status as this type of object, since it is necessary to explain what the literary work is in the isolated state. However, the reader, being a perceiving link, causes noticeable fluctuations in the literary work and adds that which is absent from the basis that R. Ingarden seeks to form. The article describes a way to solve this problem. Scientific novelty of the study lies in conducting a detailed analysis of the layers of the literary work involving achievements of the phenomenological method and in describing the reader’s influence on the above-mentioned layers. As a result, it is proved that the literary work has an objective basis in the form of layers that characterise the structure of the work and that literature is redundant in nature, which is demonstrated by introduction of the notion of concretisation describing formation of the meaning of the literary work by the reader.

Awareness improvement of things that go right by the analytical discussion of work fluctuation as SAFETY-II approach

Awareness improvement of things that go right by the analytical discussion of work fluctuation as SAFETY-II approach

Work fluctuations due to partial thermalizations in two-level systems

We study work extraction processes mediated by finite-time interactions with an ambient bath-partial thermalizations-as continuous-time Markov processes for two-level systems. Such a stochastic process results in fluctuations in the amount of work that can be extracted and is characterized by the rate at which the system parameters are driven in addition to the rate of thermalization with the bath. We analyze the distribution of work for the case in which the energy gap of a two-level system is driven at a constant rate. We derive analytic expressions for average work and a lower bound for the variance of work showing that such processes cannot be fluctuation-free in general. We also observe that an upper bound for the Monte Carlo estimate of the variance of work can be obtained using Jarzynski's fluctuation-dissipation relation for systems initially in equilibrium. Finally, we analyze work extraction cycles by modifying the Carnot cycle, incorporating processes involving partial thermalizations, and we obtain efficiency at maximum power for such finite-time work extraction cycles under different sets of constraints.

Second law of thermodynamics for batteries with vacuum state

In stochastic thermodynamics work is a random variable whose average is bounded by the change in the free energy of the system. In most treatments, however, the work reservoir that absorbs this change is either tacitly assumed or modelled using unphysical systems with unbounded Hamiltonians (i.e. the ideal weight). In this work we describe the consequences of introducing the ground state of the battery and hence — of breaking its translational symmetry. The most striking consequence of this shift is the fact that the Jarzynski identity is replaced by a family of inequalities. Using these inequalities we obtain corrections to the second law of thermodynamics which vanish exponentially with the distance of the initial state of the battery to the bottom of its spectrum. Finally, we study an exemplary thermal operation which realizes the approximate Landauer erasure and demonstrate the consequences which arise when the ground state of the battery is explicitly introduced. In particular, we show that occupation of the vacuum state of any physical battery sets a lower bound on fluctuations of work, while batteries without vacuum state allow for fluctuation-free erasure.

Thermodynamics of structure-forming systems

Structure-forming systems are ubiquitous in nature, ranging from atoms building molecules to self-assembly of colloidal amphibolic particles. The understanding of the underlying thermodynamics of such systems remains an important problem. Here, we derive the entropy for structure-forming systems that differs from Boltzmann-Gibbs entropy by a term that explicitly captures clustered states. For large systems and low concentrations the approach is equivalent to the grand-canonical ensemble; for small systems we find significant deviations. We derive the detailed fluctuation theorem and Crooks’ work fluctuation theorem for structure-forming systems. The connection to the theory of particle self-assembly is discussed. We apply the results to several physical systems. We present the phase diagram for patchy particles described by the Kern-Frenkel potential. We show that the Curie-Weiss model with molecule structures exhibits a first-order phase transition.

Odd-parity spin-loop-current order mediated by transverse spin fluctuations in cuprates and related electron systems

Unconventional symmetry-breaking phenomena due to nontrivial order parameters attract increasing attention in strongly correlated electron systems. Here, we predict theoretically the occurrence of nanoscale spontaneous spin-current, called the spin loop-current (sLC) order, as a promising origin of the pseudogap and electronic nematicity in cuprates. We reveal that the sLC is driven by the odd-parity electron-hole condensation that are mediated by transverse spin fluctuations around the pseudogap temperature $T^*$. At the same temperature, odd-parity magnon pair condensation occurs. The sLC order is "hidden" in that neither internal magnetic field nor charge density modulation is induced, whereas the predicted sLC with finite wavenumber naturally gives the Fermi arc structure. In addition, the fluctuations of sLC order work as attractive pairing interaction between adjacent hot spots, which enlarges the d-wave superconducting transition temperature $T_c$. The sLC state will be a key ingredient in understanding the pseudogap, electronic nematicity as well as superconductivity in cuprates and other strongly correlated metals.

Work fluctuation theorem for a Brownian particle in a nonconfining potential

Using the Feynman-Kac formula, a work fluctuation theorem for a Brownian particle in a nonconfining potential, e.g., a potential well with finite depth, is derived. The theorem yields aninequality that puts a lower bound on the average work needed to change the potential in time.In comparison to the Jarzynski equality, which holds for confining potentials, an additional termdescribing a form of energy related to the never ending diffusive expansion appears.

Thermodynamic uncertainty relations for bosonic Otto engines.

We study two-mode bosonic engines undergoing an Otto cycle. The energy exchange between the two bosonic systems is provided by a tunable unitary bilinear interaction in the mode operators modeling frequency conversion, whereas the cyclic operation is guaranteed by relaxation to two baths at different temperatures after each interacting stage. By means of a two-point-measurement approach we provide the joint probability of the stochastic work and heat. We derive exact expressions for work and heat fluctuations, identities showing the interdependence among average extracted work, fluctuations, and efficiency, along with thermodynamic uncertainty relations between the signal-to-noise ratio of observed work and heat and the entropy production. We outline how the presented approach can be suitably applied to derive thermodynamic uncertainty relations for quantum Otto engines with alternative unitary strokes.

Thermodynamics of Minimal Coupling Quantum Heat Engines

The minimal-coupling quantum heat engine is a thermal machine consisting of an explicit energy storage system, heat baths, and a working body, which alternatively couples to subsystems through discrete strokes --- energy-conserving two-body quantum operations. Within this paradigm, we present a general framework of quantum thermodynamics, where a work extraction process is fundamentally limited by a flow of non-passive energy (ergotropy), while energy dissipation is expressed through a flow of passive energy. It turns out that small dimensionality of the working body and a restriction only to two-body operations make the engine fundamentally irreversible. Our main result is finding the optimal efficiency and work production per cycle within the whole class of irreversible minimal-coupling engines composed of three strokes and with the two-level working body, where we take into account all possible quantum correlations between the working body and the battery. One of the key new tools is the introduced ``control-marginal state" --- one which acts only on a working body Hilbert space, but encapsulates all features regarding work extraction of the total working body-battery system. In addition, we propose a generalization of the many-stroke engine, and we analyze efficiency vs extracted work trade-offs, as well as work fluctuations after many cycles of the running of the engine.

Geometry of Work Fluctuations versus Efficiency in Microscopic Thermal Machines.

When engineering microscopic machines, increasing efficiency can often come at a price of reduced reliability due to the impact of stochastic fluctuations. Here we develop a general method for performing multiobjective optimization of efficiency and work fluctuations in thermal machines operating close to equilibrium in either the classical or quantum regime. Our method utilizes techniques from thermodynamic geometry, whereby we match optimal solutions to protocols parametrized by their thermodynamic length. We characterize the optimal protocols for continuous-variable Gaussian machines, which form a crucial class in the study of thermodynamics for microscopic systems.

Work fluctuations in a generalized Gaussian active bath

We theoretically investigate the dynamics and work distribution of a Brownian particle in a Gaussian active bath. By modeling the active noise as a generalized form of Ornstein–Uhlenbeck process (OUP), we show that the dynamics approaches asymptotically to a superdiffusive regime. Two protocols are considered to perform work on the system, and exact expressions for the probability distribution function (PDF) of work are obtained. Further, we show, by employing the large deviation principle (LDP), that the PDF follows an anomalous scaling with time, in contrast to the normal LDP. Then, fluctuation relations (FR) of work are studied to find that the transient FR does not exist, but a non-conventional FR emerges in the long-time limit. Also, the known results for the usual OUP bath are recovered.

First law of quantum field thermodynamics

We study the notion of work fluctuations in quantum field theory, highlighting that the most common definitions used in finite-dimensional quantum systems cannot be applied to quantum field theory (QFT). Then we propose work distributions that are compatible with QFT and we show that they satisfy the first law of thermodynamics up to second moments. We also show how these distributions satisfy Crooks theorem and provide a fully non-perturbative thermodynamic analysis of spacetime localized unitary processes on a quantum field.

Predictors of decent work across time: Testing propositions from Psychology of Working Theory

The goal of the current study was to examine longitudinal relations among predictors of decent work within Psychology of Working Theory (PWT). Data were collected from a large group of employed adults (N = 1540) at three-time points over six months. Multilevel modeling was used to test for the between and within-person effects of four predictor variables (economic constraints, marginalization experiences, work volition, career adaptability) on decent work. Significant between and within-person effects on decent work existed for all four predictor variables. However, within-person effects of economic constraints and marginalization on work volition and career adaptability were nonsignificant. These findings indicate that when considering sample level averages (between-person effects), theory consistent effects were found in connecting these variables across time. Work volition, in particular, was the most robust predictor of decent work and was the most robust mediator connecting economic constraints and marginalization experiences to decent work. When considering individual participant variability across time (within-person effects), it appears that changes from mean scores in structural and psychological factors both predict fluctuations in decent work. However, psychological factors do not mediate the effects of structural factors. Implications for research, practice, and theory are discussed. Public significance statementThis is the first known study to examine how specific variables may relate to the securement of decent work over time. Findings suggest that feeling a sense of choice in one's career is most predictive of viewing one's job as decent. However, changes in an individual's perception of economic constraints and marginalization may also affect perceptions of decent work.

Gamma estimator of Jarzynski equality for recovering binding energies from noisy dynamic data sets

A fundamental problem in thermodynamics is the recovery of macroscopic equilibrated interaction energies from experimentally measured single-molecular interactions. The Jarzynski equality forms a theoretical basis in recovering the free energy difference between two states from exponentially averaged work performed to switch the states. In practice, the exponentially averaged work value is estimated as the mean of finite samples. Numerical simulations have shown that samples having thousands of measurements are not large enough for the mean to converge when the fluctuation of external work is above 4 kBT, which is easily observable in biomolecular interactions. We report the first example of a statistical gamma work distribution applied to single molecule pulling experiments. The Gibbs free energy of surface adsorption can be accurately evaluated even for a small sample size. The values obtained are comparable to those derived from multi-parametric surface plasmon resonance measurements and molecular dynamics simulations.

Work as an external quantum observable and an operational quantum work fluctuation theorem

We propose a definition of externally measurable quantum work in driven systems. Work is given as a quantum observable on a control device which is forcing the system and can be determined without knowledge of the system Hamiltonian $H_\mathcal{S}$. We argue that quantum work fluctuation theorems which rely on the knowledge of $H_\mathcal{S}$ are of little practical relevance, contrary to their classical counterparts. Using our framework, we derive a fluctuation theorem which is operationally accessible and could in principle be implemented in experiments to determine bounds on free energy differences of unknown systems.

Reaching and violating thermodynamic uncertainty bounds in information engines

Thermodynamic uncertainty relations (TURs) set fundamental bounds on the fluctuation and dissipation of stochastic systems. Here, we examine these bounds, in experiment and theory, by exploring the entire phase space of a cyclic information engine operating in a nonequilibrium steady state. Close to its maximal efficiency, we find that the engine violates the original TUR. This experimental demonstration of TUR violation agrees with recently proposed softer bounds: The engine satisfies two generalized TUR bounds derived from the detailed fluctuation theorem with feedback control and another bound linking fluctuation and dissipation to mutual information and Renyi divergence. We examine how the interplay of work fluctuation and dissipation shapes the information conversion efficiency of the engine, and find that dissipation is minimal at a finite noise level, where the original TUR is violated.