The second law of thermodynamics in the quantum Brownian oscillator at an arbitrary temperature

Kim, Ilki; Mahler, Guenter

doi:10.1140/epjb/e2007-00354-5

Cited by 13 publications

(31 citation statements)

References 21 publications

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“…However, in case of strong system-reservoir interactions, finding definitions for heat, work, entropy, and entropy production, which satisfy the basic laws of thermodynamics is an open problem. Each proposal has its own limitations [16][17][18][19][20][21][22][23], even at equilibrium [24][25][26][27][28][29][30]. Reversible transformations, for instance, are never explicitly characterized.…”

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confidence: 99%

Quantum Thermodynamics: A Nonequilibrium Green’s Function Approach

2015

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We establish the foundations of a nonequilibrium theory of quantum thermodynamics for noninteracting open quantum systems strongly coupled to their reservoirs within the framework of the nonequilibrium Green's functions. The energy of the system and its coupling to the reservoirs are controlled by a slow external time-dependent force treated to first order beyond the quasistatic limit. We derive the four basic laws of thermodynamics and characterize reversible transformations. Stochastic thermodynamics is recovered in the weak coupling limit. DOI: 10.1103/PhysRevLett.114.080602 PACS numbers: 05.70.Ln, 05.60.Gg Nonequilibrium thermodynamics of open quantum systems is a powerful tool for the study of mesoscopic and nanoscale systems. It allows one to reliably assess the performance of energy-converting devices such as thermoelectrics or photoelectrics, by identifying the system entropy production. It enables one to meaningfully compare these different devices by discriminating the systemspecific features from the universal ones and to appraise the role of quantum effects. It can also be used to verify the thermodynamic consistency of approximation schemes. Such a theory is nowadays available for systems weakly interacting with their surrounding [1][2][3][4][5][6], where it has proven very useful [7][8][9][10][11][12][13][14][15]. However, in case of strong system-reservoir interactions, finding definitions for heat, work, entropy, and entropy production, which satisfy the basic laws of thermodynamics is an open problem. Each proposal has its own limitations [16][17][18][19][20][21][22][23], even at equilibrium [24][25][26][27][28][29][30]. Reversible transformations, for instance, are never explicitly characterized. Establishing a consistent nonequilibrium thermodynamics for open quantum systems strongly coupled to their surrounding is therefore an important step towards a more realistic thermodynamic description of mesoscopic and nanoscale devices. It is also essential to improve our understanding of the microscopic foundations of thermodynamics.In this Letter, we use the nonequilibrium Green's functions (NEGF) to establish a fully consistent nonequilibrium thermodynamic description of a fermionic single quantum level strongly coupled to multiple fermionic reservoirs. A slow time-dependent driving force controls the level energy as well as the system-reservoir interaction. We propose definitions for the particle number, the energy, and the entropy of the system, as well as for entropy production, heat, and work, which give rise to a consistent zeroth, first, second, and third law. These definitions can be seen as energy resolved versions of the weak coupling definitions used in stochastic thermodynamics. An interesting outcome of our approach is that the general form of the energy and particle currents is different from the standard form used in the NEGF and cannot be expressed as an expectation value of operators. We recover the known expressions when considering nonequilibrium steady states (i.e., in absenc...

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confidence: 99%

Quantum Thermodynamics: A Nonequilibrium Green’s Function Approach

2015

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“…(13), (14), (16), and (17) the work out put and the ef fi ciency for a two-state quan tum heat en gine may be writ ten as: If the two-eigenstates sys tem is al lowed to cou ple to the heat baths in pro cess 1-2 and pro cess 3-4, the ther mal equi lib rium prob a bil i ties with the ther mal equi lib rium Gibbs dis tri butions may be writ ten as [17]: …”

Section: Two-state Quan Tum Heat En Ginementioning

confidence: 99%

“…Its work out put and ef fi ciency may be ob tained by the first law of ther mo dy nam ics and the clas si cal ideal gas equa tion of state. How ever, a quan tum heat engine [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] obeys the laws of quan tum me chan ics. The in flu ence of the quan tum char ac ter is tics of the work ing fluid on the per for mance of the cy cle must be con sid ered.…”

Section: Introductionmentioning

confidence: 99%

Work output and efficiency of a reversible quantum Otto cycle

Wu¹,

Yang²,

Chen³

et al. 2010

Therm. sci.

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An ide al ized re vers ible Otto cy cle work ing with a sin gle quan tum me chan i cal par ticle con tained in a po ten tial well is in ves ti gated based on the Schrödinger equa tion in this pa per. The model of a re vers ible quan tum Otto cy cle, which con sists of two re vers ible adi a batic and two con stant-well widen branches, is es tab lished. As an ex am ple, we cal cu late a par tic u larly sim ple case in which only two of the eigenstates of the po ten tial well con trib ute to the wave-func tion in the well. The rela tion ship be tween the op ti mal dimensionless work out put W* vs. the ef fi ciency h for the two-eigenstate sys tem is de rived. The ef fi ciency of this quan tum cy cle is shown to equal that of a clas si cal re vers ible Otto cy cle be cause quan tum dy nam ics is re vers ible. In tro duc tionA heat en gine is an im por tant en ergy con ver sion de vice. A clas si cal heat en gine converts heat en ergy into me chan i cal work by means of a gas that ex pands and pushes a pis ton in a cyl in der. For a clas si cal ther mo dy namic heat en gine the en ergy re quired is gen er ally from a high-tem per a ture heat res er voir. Its work out put and ef fi ciency may be ob tained by the first law of ther mo dy nam ics and the clas si cal ideal gas equa tion of state. How ever, a quan tum heat engine [1-20] obeys the laws of quan tum me chan ics. The in flu ence of the quan tum char ac ter is tics of the work ing fluid on the per for mance of the cy cle must be con sid ered.The quan tum heat en gine at tracts much at ten tion due to its spe cial fea tures. Pres ent tech nol ogy now al lows for the prob ing and/or re al iza tion of quan tum me chan i cal sys tems of micro scopic and even mac ro scopic sizes (like those of su per con duc tors, Bose-Ein stein con densates, etc.) which can also be re stricted to a rel a tively small num ber of en ergy states. It is in terest ing that the quan tum cy cles an a lyzed can be sim i lar to var i ous as pects of clas si cal ther mo dy namic cy cles such as Car not [18,20], Stirling [5,7,21], Otto [22][23][24], Brayton [16,17, Wu, F., et al.: Work Output and Efficiency of a Reversible Quantum Otto Cycle

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“…By using (15) and changing the sum in an integral, the first-order-correction term can then be obtained as…”

Section: Free Energy Of An Atom Inside a Knbmentioning

confidence: 99%

“…A Kerr nonlinear blackbody: a rectangular Kerr nonlinear crystal enclosed by perfectly conducting walls and kept at a constant temperature; there is a small hole in a wall is more, many other researchers in the community of thermodynamics have shown that the basic laws of thermodynamics might not be violated in many cases [12][13][14][15][16][17]. Up to now, it is till a hot topic.…”

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confidence: 99%

Thermodynamic Properties of an Atom Inside a Kerr Nonlinear Blackbody

et al. 2010

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Thermodynamic properties of a Kerr nonlinear blackbody (KNB) are investigated. It is found that below a transition temperature T c , the free energy of a KNB radiation is larger than that in a normal blackbody. At the transition from KNB radiation state to a normal blackbody radiation state, the photon system undergoes a first-order phase transition. The thermodynamic system of an atom interacting with a KNB radiation bath is also investigated by using a thermodynamic perturbation theory. It is found that below a transition temperature T c , the increment of the free energy of the atom is larger than that in a normal blackbody. Above T c , the KNB becomes a normal blackbody, and the properties in a KNB turn to be the same as those in normal blackbody radiation.

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The second law of thermodynamics in the quantum Brownian oscillator at an arbitrary temperature

Cited by 13 publications

References 21 publications

Quantum Thermodynamics: A Nonequilibrium Green’s Function Approach

Quantum Thermodynamics: A Nonequilibrium Green’s Function Approach

Work output and efficiency of a reversible quantum Otto cycle

Thermodynamic Properties of an Atom Inside a Kerr Nonlinear Blackbody

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