Information and Entropy in Quantum Brownian Motion

Hörhammer, Christian; Büttner, H.

doi:10.1007/s10955-008-9640-x

Cited by 59 publications

(85 citation statements)

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“…(8) for the thermodynamic partition function of an open quantum system the result that is well known to those working on strong quantum dissipation [12,[18][19][20][21][22][23][24][25][26][27][28][29], namely:…”

Section: Selected For a Viewpoint In Physics P H Y S I C A L R E V I mentioning

confidence: 99%

“…Note that the thermodynamics that follows from the partition function Z S ðtÞ comprises the equilibrium properties of the open quantum system in a consistent manner including the influence of environment and coupling [11,12,[18][19][20][21]: In particular, the thermodynamic functions that follow from this thermodynamic partition function do not violate any known thermodynamic law.…”

Section: Selected For a Viewpoint In Physics P H Y S I C A L R E V I mentioning

confidence: 99%

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Fluctuations in open systems

Ritort¹

2009

Physics

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Based on the observation that the thermodynamic equilibrium free energy of an open quantum system in contact with a thermal environment is the difference between the free energy of the total system and that of the bare environment, the validity of the Crooks theorem and of the Jarzynski equality is extended to open quantum systems. No restrictions on the nature of the environment or on the strength of the coupling between system and environment need to be imposed. This free energy entering the Crooks theorem and the Jarzynski equality is closely related to the Hamiltonian of mean force that generalizes the classical statistical mechanical concept of the potential of mean force. DOI: 10.1103/PhysRevLett.102.210401 PACS numbers: 05.30.Àd, 05.70.Ln Since its formulation in 1997, the classical nonequilibrium work relation by Jarzynski [1] (now commonly referred to as the Jarzynski equality)has continued to raise questions and concerns on its range of validity and applicability. Here, w denotes the work performed on a system when some parameters of this system are changed according to a prescribed protocol. This work is given by the difference of the energies contained in the system at the end and at the beginning of the protocol. Initially, the system is supposed to be prepared in a thermal equilibrium state at the inverse temperature .The brackets hÁi denote a nonequilibrium average over many repetitions of this process, running under the same protocol. According to the Jarzynski equality, the average of the exponentiated negative work is independent of the details of the protocol and solely determined by the thermal equilibrium free energy difference ÁF between the initial equilibrium state and a hypothetical equilibrium state at the initial temperature and those parameter values that are reached at the end of the protocol. In the mentioned Letter [1], the validity of this equality was demonstrated within a classical statistical approach for isolated systems which initially are in the required equilibrium state at inverse temperature and also for classical systems that stay in weak contact with a thermal bath during the protocol. Considerable effort has been devoted to the development of the quantum version of Eq. (1) where p t f ;t 0 ðwÞ denotes the probability density function (PDF) of work performed by the parameter changes according to a protocol running between the initial time t 0 and final time t f . The PDF of work for the reversed protocol is denoted by p t 0 ;t f ðwÞ. All these attempts refer to quantum isolated or weakly coupled systems with Hamiltonian or Markovian dynamics, respectively [3][4][5][6][7][8][9]. The proof of the validity of Eqs. (1) and (2) in the quantum case with weak coupling, allowing for an otherwise general non-Markovian dynamics of the open quantum dynamics and arbitrary force protocols, was provided only recently in Ref.[10]. The applicability of Eqs. (1) and (2) to the case of weak coupling is consistent with the construction of quantum and classical statistical mechanics wh...

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Section: Selected For a Viewpoint In Physics P H Y S I C A L R E V I mentioning

confidence: 99%

Section: Selected For a Viewpoint In Physics P H Y S I C A L R E V I mentioning

confidence: 99%

Fluctuations in open systems

Ritort¹

2009

Physics

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“…Though considerable attention has recently been focused on identifying consistent definitions of heat, work, and internal energy in the strong coupling regime [19,[30][31][32], and on formulating the second law by studying strong coupling versions of quantum fluctuation relations [33][34][35], or entropy and entropy production [36][37][38][39], a consensus on a consistent approach to analysing thermodynamic cycles beyond weak reservoir coupling is arguably still lacking. In fact, there are few studies of heat engines in this regime to date, with some exceptions being Refs.…”

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confidence: 99%

Performance of a quantum heat engine at strong reservoir coupling

2017

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We study a quantum heat engine at strong coupling between the system and the thermal reservoirs. Exploiting a collective coordinate mapping, we incorporate system-reservoir correlations into a consistent thermodynamic analysis, thus circumventing the usual restriction to weak coupling and vanishing correlations. We apply our formalism to the example of a quantum Otto cycle, demonstrating that the performance of the engine is diminished in the strong coupling regime with respect to its weakly coupled counterpart, producing a reduced net work output and operating at a lower energy conversion efficiency. We identify costs imposed by sudden decoupling of the system and reservoirs around the cycle as being primarily responsible for the diminished performance, and define an alternative operational procedure which can partially recover the work output and efficiency. More generally, the collective coordinate mapping holds considerable promise for wider studies of thermodynamic systems beyond weak reservoir coupling.

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“…which could probably explain the observed differences between the thermodynamic and von Neumann entropy definitions at low temperature (Hörhammer and Büttner 2008 …”

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confidence: 97%

Nonlinear Theory of Quantum Brownian Motion

Tsekov

2008

Int J Theor Phys

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A nonlinear theory of quantum Brownian motion in classical environment is developed based on a thermodynamically enhanced nonlinear Schrödinger equation. The latter is transformed via the Madelung transformation into a nonlinear quantum Smoluchowski-like equation, which is proven to reproduce key results from quantum and classical physics. The application of the theory to a free quantum Brownian particle results in a nonlinear dependence of the position dispersion on time, being quantum generalization of the Einstein law of Brownian motion. It is shown that the time of decoherence for the transition from quantum to classical diffusion is proportional to the square of the thermal de Broglie wavelength divided by the Einstein diffusion constant.Brownian motion is the permanent irregular movement of a particle immersed in a medium. Its rigorous description requires joint consideration of the coupled dynamics of the Brownian particle and the medium, usually referred as thermal bath. Fundamental problems appear in the Brownian motion theory if the quantum effects become important. For instance, at time larger than the classical momentum relaxation time the Brownian motion of a quantum particle in a classical environment is regularly described by the classical Einstein law

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Information and Entropy in Quantum Brownian Motion

Cited by 59 publications

References 32 publications

Fluctuations in open systems

Fluctuations in open systems

Performance of a quantum heat engine at strong reservoir coupling

Nonlinear Theory of Quantum Brownian Motion

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