arXiv subjects

Peter Talkner

Publications and source records attributed to Peter Talkner.

At least 19 recordsLinked to original sources

arXiv2022

Charging quantum batteries via Otto machines: The influence of monitoring

The charging of a quantum battery by a four-stroke quantum machine that works either as an engine or a refrigerator is investigated. The presented analysis provides the energetic behavior of the combined system in terms of the heat and workflows of the machine, the average, and variance of the battery's energy as well as the coherent and incoherent parts of its ergotropy. To monitor the battery state its energy is measured either after the completion of any cycle or after a prescribed number of cycles is carried out. The resulting battery performances greatly differ for those two cases. During the first charging epoch with an engine, the regular measurements speed up the charging, whereas the gain of ergotropy is more pronounced in the absence of measurements. In a later stage, the engine fails to work as such while it still continues charging the battery that eventually reaches the maximally charged state in the absence of intermediate measurements and a suboptimally charged state for a periodically measured battery. For a refrigerator, the charging of the measured battery also proceeds faster during the first epoch. Only during the second stage when the machine fails to extract heat from the cold bath the influence of the measurements become less pronounced leading to rather similar asymptotic states for the two measurement scenarios.

quant-ph↗

arXiv2021

Quasistatic work processes: When slowness implies certainty

Two approaches are outlined to characterize the fluctuation behavior of work applied to a system by a slow change of a parameter. One approach uses the adiabatic theorems of quantum and classical mechanics, the other one is based on the behavior of the correlations of the generalized coordinate that is conjugate to the changed parameter. Criteria are obtained under which the work done on small thermally isolated as well as on open systems ceases to fluctuate in a quasistatic process.

cond-mat.stat-mech↗

arXiv2021

Monitoring quantum Otto engines

Unlike classical systems, a measurement performed on a quantum system always alters its state. In this work, the impacts of two diagnostic schemes to determine the performance of quantum Otto heat engines are compared: In one scheme, the energy of the engine's working substance is measured after each stroke (repeated measurements), and in the other one, the energies after each stroke are recorded in one or two pointer states and measured only after the completion of a prescribed number of cycles (repeated contacts). A single pointer state suffices if one is only interested in either work or heat. For joint work and heat diagnostics, two pointers are needed. These schemes are applied to Otto engines, whose working substance consists of a two-level system. Depending on the engine protocol, the duration of a single cycle may be infinite or finite. Because in the repeated contact scheme, the number of measurements is drastically reduced compared to the repeated measurement scheme, the quantum coherence after and during the contact diagnostics is much better maintained than repeated measurements that destroy any coherence at the end of each stroke. We demonstrate that maximum power, reliability, and efficiency of the engine in the presence of repeated contacts typically outperform these figures of merit of repeated measurements. Due to the improved coherence persistence, heat engines with a finite cycle duration require a larger number of cycles to reach a periodically asymptotic state. Overall, our results document the importance of taking into account the particular nature of diagnostic tools for monitoring and testing purposes but also for feedback control, both in theory and experiment.

quant-ph↗

arXiv2020

Comment on "Measurability of nonequilibrium thermodynamics in terms of the Hamiltonian of mean force"

In a recent paper [P. Strasberg and M. Esposito, Phys. Rev. E {\bf 101}, 050101(R) (2020)] an attempt is presented to formulate the nonequilibrium thermodynamics of an open system in terms of the Hamiltonian of mean force. The purpose of the present comment is to clarify severe restrictions of this approach and also to stress that recently noted ambiguities [P. Talkner and P. H\"anggi, Phys. Rev. E {\bf 94}, 022143 (2016)] of fluctuating thermodynamic potentials cannot be removed in the suggested way.

cond-mat.stat-mech↗

arXiv2020

To Measure, or Not to Measure, That is the Question

A method is proposed that allows one to infer the sum of the values of an observable taken during contacts with a pointer state. Hereby the state of the pointer is updated while contacted with the system and remains unchanged between contacts while the system evolves in time. After a prescribed number of such contacts the position of the pointer is determined by means of a projective measurement. The outcome is specified in terms of a probability distribution function for unitary and Markovian dissipative dynamics and compared with the results of the same number of generalized Gaussian measurements of the considered observable. As a particular example a qubit is considered with an observable contacting to the pointer that does not commute with the system Hamiltonian.

cond-mat.stat-mech↗

arXiv2019

{\it Colloquium:} Statistical Mechanics and Thermodynamics at Strong Coupling: Quantum and Classical

The statistical mechanical description of small systems staying in thermal equilibrium with an environment can be achieved by means of the Hamiltonian of mean force. In contrast to the reduced density matrix of an open quantum system, or the reduced phase-space probability density function of a classical open system, the Hamiltonian of mean force not only characterizes the reduced state but also contains full information about the thermodynamics of the considered open system. The resulting thermodynamic potentials all assume the form as the difference of the potentials for the total system and the bare environment in the absence of the system. In contrast to work as a mechanical notion, one faces several problems with the definition of heat which turns out to be largely ambiguous in the case of strong coupling between system and environment. The general theory of the thermodynamics of open systems, in particular, in view of strong coupling, is reviewed and illustrated with several examples. The vagueness of heat is discussed in the context of the ambiguities in the definitions of a fluctuating internal energy and other fluctuating thermodynamic potentials.

cond-mat.stat-mech↗

arXiv2019

Quantum Statistical Enhancement of the Collective Performance of Multiple Bosonic Engines

We consider an ensemble of indistinguishable quantum machines and show that quantum statistical effects can give rise to a genuine quantum enhancement of the collective thermodynamic performance. When multiple indistinguishable bosonic work resources are coupled to an external system, the internal energy change of the external system exhibits an enhancement arising from permutation symmetry in the ensemble, which is absent when the latter consists of distinguishable work resources.

quant-ph↗

arXiv2018

Generalized energy measurements and quantum work compatible with fluctuation theorems

The probability densities of work that can be exerted on a quantum system initially staying in thermal equilibrium are constrained by the fluctuation relations of Jarzynski and Crooks, when the work is determined by two projective energy measurements. We investigate the question whether these fluctuation relations may still hold if one employs generalized energy measurements rather than projective ones. Restricting ourselves to a class of universal measurements which are independent of several details of the system on which the work is done, we find sets of necessary and sufficient conditions for the Jarzynski equality and the Crooks relation. The Jarzynski equality requires perfect accuracy for the initial measurement, while the final one can be erroneous. On the other hand, the Crooks relation can only tolerate a depolarizing channel as a deviation from the projective measurement for systems with a finite dimensional Hilbert space. For a separable infinite-dimensional space only projective measurements are compatible with the Crooks relation. The results we have obtained significantly extend those of [Venkatesh, Watanabe, and Talkner, New J. Phys. 16, 015032 (2014)] as well as avoid some errors present there.

quant-ph↗

arXiv2018

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.

cond-mat.stat-mech↗

arXiv2017

Molecular Hydrodynamics: Vortex Formation and Sound Wave Propagation

In the present study, quantitative feasibility tests of the hydrodynamic description of a two-dimensional fluid at the molecular level are performed, both with respect to length and time scales. Using high-resolution fluid velocity data obtained from extensive molecular dynamics simulations, we computed the transverse and longitudinal components of the velocity field by the Helmholtz decomposition and compared them with those obtained from the linearized Navier-Stokes (LNS) equations with time-dependent transport coefficients. By investigating the vortex dynamics and the sound wave propagation in terms of these field components, we confirm the validity of the LNS description for times comparable to or larger than several mean collision times. The LNS description still reproduces the transverse velocity field accurately at smaller times, but it fails to predict characteristic patterns of molecular origin visible in the longitudinal velocity field. Based on these observations, we validate the main assumptions of the mode-coupling approach. The assumption that the velocity autocorrelation function can be expressed in terms of the fluid velocity field and the tagged particle distribution is found to be remarkably accurate even for times comparable to or smaller than the mean collision time. This suggests that the hydrodynamic-mode description remains valid down to the molecular scale.

physics.flu-dyn↗

arXiv2017

Nature of self-diffusion in two-dimensional fluids

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function using a consistency equation relating these quantities. We numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the velocity autocorrelation function. An asymptotic decay law of the velocity autocorrelation function resembles the previously known self-consistent form, $1/(t\sqrt{\ln t})$, however with a rescaled time.

cond-mat.soft↗

arXiv2017

Role of work in matter exchange between finite quantum systems

Close to equilibrium, the exchange of particles and heat between macroscopic systems at different temperatures and different chemical potentials is known to be governed by a matrix of transport coefficients which is positive and symmetric. We investigate the amounts of heat and particles that are exchanged between two small quantum systems within a given time, and find them characterized by a transport matrix which neither needs to be symmetric nor positive. At larger times even spontaneous transport can be observed in the total absence of temperature and chemical potential differences provided that the two systems are different in size. All these deviations from standard transport behavior can be attributed to the fact that work is done on the system in the processes contacting and separating those parts of the system that initially possess different temperatures and chemical potentials. The standard transport properties are recovered for vanishing work and also in the limit of large systems and sufficiently large contact times. The general results are illustrated by an example.

cond-mat.stat-mech↗

arXiv2017

Single-Temperature Quantum Engine Without Feedback Control

A cyclically working quantum mechanical engine that operates at a single temperature is proposed. Its energy input is delivered by a quantum measurement. The functioning of the engine does not require any feedback control. We analyze work, heat, and the efficiency of the engine for the case of a working substance that is governed by the laws of quantum mechanics and that can be adiabatically compressed and dilated. The obtained general expressions are exemplified for a spin in an adiabatically changing magnetic field and a particle moving in a potential with slowly changing shape.

cond-mat.stat-mech↗

arXiv2017

Work distributions for random sudden quantum quenches

The statistics of work performed on a system by a sudden random quench is investigated. Considering systems with finite dimensional Hilbert spaces we model a sudden random quench by randomly choosing elements from a Gaussian unitary ensemble (GUE) consisting of hermitean matrices with identically, Gaussian distributed matrix elements. A probability density function (pdf) of work in terms of initial and final energy distributions is derived and evaluated for a two-level system. Explicit results are obtained for quenches with a sharply given initial Hamiltonian, while the work pdfs for quenches between Hamiltonians from two independent GUEs can only be determined in explicit form in the limits of zero and infinite temperature.

quant-ph↗

arXiv2016

Quantum Performance of Thermal Machines over Many Cycles

The performance of quantum heat engines is generally based on the analysis of a single cycle. We challenge this approach by showing that the total work performed by a quantum engine need not be proportional to the number of cycles. Furthermore, optimizing the engine over multiple cycles leads to the identification of scenarios with a quantum enhancement. We demonstrate our findings with a quantum Otto engine based on a two-level system as the working substance that supplies power to an external oscillator.

cond-mat.stat-mech↗

arXiv2016

Non-monotonic temperature dependence of chaos-assisted diffusion in driven periodic systems

The spreading of a cloud of independent Brownian particles typically proceeds more effectively at higher temperatures, as it derives from the commonly known Sutherland-Einstein relation for systems in thermal equilibrium. Here, we report on a non-equilibrium situation in which the diffusion of a periodically driven Brownian particle moving in a periodic potential decreases with increasing temperature within a finite temperature window. We identify as the cause for this non-intuitive behaviour a dominant deterministic mechanism consisting of a few unstable periodic orbits embedded into a chaotic attractor together with thermal noise-induced dynamical changes upon varying temperature. The presented analysis is based on extensive numerical simulations of the corresponding Langevin equation describing the studied setup as well as on a simplified stochastic model formulated in terms of a three-state Markovian process. Because chaos exists in many natural as well as in artificial systems representing abundant areas of contemporary knowledge, the described mechanism may potentially be discovered in plentiful different contexts.

cond-mat.stat-mech↗

arXiv2016

Open system trajectories specify fluctuating work but not heat

Based on the explicit knowledge of a Hamiltonian of mean force, the classical statistical mechanics and equilibrium thermodynamics of open systems in contact with a thermal environment at arbitrary interaction strength can be formulated. Even though the Hamiltonian of mean force uniquely determines the equilibrium phase space probability density of a strongly coupled open system the knowledge of this probability density alone is insufficient to determine the Hamiltonian of mean force, needed in constructing the underlying statistical mechanics and thermodynamics. We demonstrate that under the assumption that the Hamiltonian of mean force is known, an extension of thermodynamic structures from the level of averaged quantities to fluctuating objects (i.e. a stochastic thermodynamics) is possible. However, such a construction undesirably involves also a vast ambiguity. This situation is rooted in the eminent lack of a physical guiding principle allowing to distinguish a physically meaningful theory out of a multitude of other equally conceivable ones.

cond-mat.stat-mech↗

arXiv2015

Aspects of work

Various approaches of defining and determining work performed on a quantum system are compared. Any operational definition of work, however, must allow for two facts, first, that work characterizes a process rather than an instantaneous state of a system, and, second, that quantum systems are sensitive to the interactions with a measurement apparatus. We compare different measurement scenarios on the basis of the resulting post-measurement states and the according probabilities for finding a particular work value. In particular, we analyze a recently proposed work-meter for the case of a Gaussian pointer state and compare it with the results obtained by two projective and, alternatively, two Gaussian measurements. In the limit of a strong effective measurement strength the work distribution of projective two energy measurements can be recovered. In the opposite limit the average of work becomes independent of any measurement. Yet the fluctuations about this value diverge. The performance of the work-meter is illustrated by the example of a spin in a suddenly changing magnetic field.

quant-ph↗