# Peter TalknerUniversität Augsburg | UNA · Institute of Physics

Peter Talkner

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227

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## Publications

Publications (227)

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...

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, and the other one is based on the behavior of the correlations of the generalized coordinate that is conjugate to the changed parameter. Criter...

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...

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 a...

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...

In a recent paper [Phys. Rev. E 101, 050101(R) (2020)PREHBM2470-004510.1103/PhysRevE.101.050101] 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 to stress that recently noted a...

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 n...

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...

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 am...

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 en...

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...

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 clear 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 f...

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 outcoupled work leads to an internal energy change of the sy...

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 gene...

In stochastic resonance, the combination of a weak signal with noise leads to its amplification and optimization¹. This phenomenon has been observed in several systems in contexts ranging from palaeoclimatology, biology, medicine, sociology and economics to physics1–9. In all these cases, the systems were either operating in the presence of thermal...

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 gene...

A protocol is proposed to generate Bell states in two non-directly interacting qubits by means of repeated measurements of the state of a central ancilla connected to both qubits. An optimal measurement rate is found that minimizes the time to stably encode a Bell state in the target qubits, being of advantage in order to reduce detrimental effects...

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 differe...

We study the quantum Brownian motion of a harmonic oscillator undergoing a sequence of generalized position measurements. Our exact analytical results capture the interplay of the measurement backaction and dissipation. Here we demonstrate that no freeze-in Zeno effect occurs upon increasing the monitoring frequency. A similar behavior is also foun...

A protocol is proposed to generate Bell states in two non-directly interacting qubits by means of repeated measurements of the state of a central ancilla connected to both qubits. An optimal measurement rate is found that minimizes the time to stably encode a Bell state in the target qubits, being of advantage in order to reduce detrimental effects...

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 fluid with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function using a consistency equation relati...

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...

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...

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 qua...

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...

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. Further, optimizing the engine over multiple cycles leads to the identification of scenarios with a quantum enhancemen...

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 per...

Diffusion is a key phenomenon in almost all branches of natural science that describes irregularity of motion. The latter can arise from two main sources. First, the dynamics of the system can be deterministically chaotic. Second, irregularity in the motion occurs due to the unavoidable presence of noise in any real setup. It is expected that the m...

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...

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 apparatu...

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 apparat...

The inhibition of the decay of a quantum system by frequent measurements is
known as quantum Zeno effect. Beyond the limit of projective measurements, the
interplay between the unitary dynamics of the system and the coupling to a
measurement apparatus becomes relevant. We explore this interplay by
considering a quantum particle moving on a one-dime...

Work in the paradigm of quantum fluctuation theorems of Crooks and Jarzynski,
is determined by projective measurements of energy at the beginning and end of
the force protocol. In analogy to classical systems, we consider an alternate
definition of work given by the integral of the supplied power determined by
integrating up the results of repeated...

Fluctuation theorems go beyond the linear response regime to describe systems far from equilibrium. But what happens to these theorems when we enter the quantum realm? The answers, it seems, are now coming thick and fast.

Based on the generalized Langevin equation for the momentum of a Brownian
particle a generalized asymptotic Einstein relation is derived. It agrees with
the well-known Einstein relation in the case of normal diffusion but continues
to hold for sub- and super-diffusive spreading of the Brownian particle's mean
square displacement. The generalized as...

Determining the work which is supplied to a system by an external agent, provides a crucial step in any experimental realization of transient fluctuation relations. This, however, poses a particular problem in the case of quantum systems. The standard procedure requires the measurement of energy at the beginning and the end of the protocol. Unfortu...

Generalized measurements of an observable performed on a quantum system during a force protocol are investigated and conditions that guarantee the validity of the Jarzynski equality and the Crooks relation are formulated. In agreement with previous studies by M. Campisi, P. Talkner, and P. Hänggi [Phys. Rev. Lett. 105, 140601 (2010); Phys. Rev. E 8...

The transient quantum fluctuation theorems of Crooks and Jarzynski restrict and relate the statistics of work performed in forward and backward forcing protocols. So far, these theorems have been obtained under the assumption that the work is determined by two projective energy measurements, one at the end, and the other one at the beginning of eac...

The work performed on a system in a microcanonical state by changes in a
control parameter is characterized in terms of its statistics. The transition
probabilities between eigenstates of the system Hamiltonians at the beginning
and the end of the parameter change obey a detailed balance-like relation from
which various forms of the microcanonical...

A Reply to the Comment by M. Campisi et al.

DOI:https://doi.org/10.1103/PhysRevE.86.059903

The estimate of free energy changes based on Bennett's acceptance ratio method is examined in several limiting cases and compared with other estimates based on the Jarzynski equality and on the Crooks relation. While the absolute amount of the dissipated work, defined as the surplus of the average work over the free energy difference, limits the pr...

In response to the recent critical comment by M. Mel\'endez and W. G. Hoover
[arXiv:1206.0188v2] on our work [M. Campisi et al., Phys. Rev. Lett. 108,
250601 (2012)], we show that their molecular dynamics simulations do not
disprove our theory but in fact convincingly corroborate it.

The transport of slightly deformable chiral objects in a uniform shear flow
is investigated. Depending on the equilibrium configuration one finds up to
four different asymptotic states that can be distinguished by a lateral drift
velocity of their center of mass, a rotational motion about the center of mass
and deformations of the object. These def...

We study the drift of suspended micro-particles in a viscous liquid pumped
back and forth through a periodic lattice of pores (drift ratchet). In order to
explain the particle drift observed in such an experiment, we present an
one-dimensional deterministic model of Stokes' drag. We show that the stability
of oscillations of particle is related to...

In response to W. G. Hoover's comment [arXiv:1204.0312v2] on our work
[arXiv:1203.5968], we show explicitly that the divergence of the velocity field
associated with the Nos\'e-Hoover equations is nonzero, implying that those
equations are not volume preserving, and hence, as often stated in the
literature, are not Hamiltonian. We further elucidate...

A logarithmic oscillator (in short, log-oscillator) behaves like an ideal thermostat because of its infinite heat capacity: When it weakly couples to another system, time averages of the system observables agree with ensemble averages from a Gibbs distribution with a temperature $T$ that is given by the strength of the logarithmic potential. The re...

We consider bosons in a harmonic trap and investigate the fluctuations of the
work performed by an adiabatic change of the trap curvature. Depending on the
reservoir conditions such as temperature and chemical potential that provide
the initial equilibrium state, the exponentiated work average (EWA) defined in
the context of the Crooks relation and...

DOI:https://doi.org/10.1103/RevModPhys.83.1653

The influence of repeated projective measurements on the dynamics of the state of a quantum system is studied as a function of the time lag τ between successive measurements. In the limit of infinitely many measurements of the occupancy of a single state the total system approaches a uniform state. The asymptotic approach to this state is exponenti...

We investigate the statistics of work performed on a noninteracting electron gas confined in a ring as a threaded magnetic field is turned on. For an electron gas initially prepared in a grand canonical state it is demonstrated that the Jarzynski equality continues to hold in this case, with the free energy replaced by the grand potential. The work...

The recently demonstrated robustness of fluctuation theorems against measurements [M. Campisi, P. Talkner, and P. Hänggi, Phys. Rev. Lett. 105, 140601 (2010).] does not imply that the probability distributions of nonequilibrium quantities, such as heat and work, remain unaffected. We determine the impact of measurements that are performed during a...

We consider N fermionic particles in a harmonic trap initially prepared in a thermal equilibrium state at temperature β^{-1} and examine the probability density function (pdf) of the work done by a magnetic field slowly varying in time. The behavior of the pdf crucially depends on the number of particles N but also on the temperature. At high tempe...

We derive an analytical expression of the second virial coefficient of d-dimensional hard sphere fluids confined to slit pores by applying Speedy and Reiss' interpretation of cavity space. We confirm that this coefficient is identical to the one obtained from the Mayer cluster expansion up to second order with respect to fugacity. The key step of b...

The quantum version of the Bochkov-Kuzovlev identity is derived on the basis of the appropriate definition of work as the difference of the measured internal energies of a quantum system at the beginning and the end of an external action on the system given by a prescribed protocol. According to the spirit of the original Bochkov-Kuzovlev approach,...

Two fundamental ingredients play a decisive role in the foundation of
fluctuation relations: the principle of microreversibility and the fact that
thermal equilibrium is described by the Gibbs canonical ensemble. Building on
these two pillars we guide the reader through a self-contained exposition of
the theory and applications of quantum fluctuati...

Brownian motion of single particles with various masses M and diameters D is
studied by molecular dynamics simulations. Besides the momentum
auto-correlation function of the Brownian particle the memory function and the
fluctuating force which enter the generalized Langevin equation of the Brownian
particle are determined and their dependence on ma...

The exactly solvable model of a one dimensional isotropic XY spin chain is employed to study the thermodynamics of open systems. For this purpose the chain is subdivided into two parts, one part is considered as the system while the rest as the environment or bath. The equilibrium properties of the system display several anomalous aspects such as n...

Calcium oscillations present one of the most important signaling mechanisms in cell biology. The standard paradigm
for the origin of calcium oscillations is dynamic, i.e. fast release of calcium from intracellular
stores is followed by slow inhibition. Yet, this very dynamic theory
for these oscillations came recently into scrutiny since the buildi...

It is shown that quantum fluctuation theorems remain unaffected if measurements of any kind and number of observables are performed during the action of a force protocol. That is, although the backward and forward probabilities entering the fluctuation theorems are both altered by these measurements, their ratio remains unchanged. This observation...

Systems where resource availability approaches a critical threshold are
common to many engineering and scientific applications and often necessitate
the estimation of first passage time statistics of a Brownian motion (Bm)
driven by time-dependent drift and diffusion coefficients. Modeling such
systems requires solving the associated Fokker-Planck...

A simple way to convert a purely random sequence of events into a signal with a strong periodic component is proposed. The
signal consists of those instants of time at which the length of the random sequence exceeds an integer multiple of a given
number. The larger this number the more pronounced the periodic behavior becomes.

The dissociation of inter- and intra-molecular bonds by force is a process that occurs regularly in biological machinery and many cellular events. Forcing such transitions in a controlled environment has also emerged as a modern practice in the laboratory for studies of the physical principles of bond lifetimes and protein unfolding. It is commonly...

We consider different Markovian embedding schemes of non-Markovian stochastic processes that are described by generalized Langevin equations and obey thermal detailed balance under equilibrium conditions. At thermal equilibrium, superdiffusive behavior can emerge if the total integral of the memory kernel vanishes. Such a situation of vanishing sta...

We illustrate recent results concerning the validity of the work fluctuation theorem in open quantum systems (Campisi et al 2009 Phys. Rev. Lett. 102 210401), by applying them to a solvable model of an open quantum system. The central role played by the thermodynamic partition function of the open quantum system, a two-level fluctuator with a stron...

We demonstrate that a finite bath fluctuation theorem of the Crooks type holds for systems that have been thermalized via weakly coupling them to a bath with energy independent finite specific heat. We show that this theorem reduces to the known canonical and microcanonical fluctuation theorems in the two respective limiting cases of infinite and v...

The large time dynamics of a periodically driven Fokker-Planck process possessing several metastable states is investigated. At weak noise transitions between the metastable states are rare. Their dynamics then represent a discrete Markovian process characterized by time dependent rates. Apart from the occupation probabilities, so-called specific p...