Dissipation: The Phase-Space Perspective

Kawai, Ryoichi; Parrondo, Juan M. R.; Broeck, C. Van den

doi:10.1103/physrevlett.98.080602

Cited by 468 publications

(589 citation statements)

References 14 publications

(20 reference statements)

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“…Under our assumptions that the bath has infinite heat capacity, the nonequilibrium expectation (5) of W dis vanishes in the adiabatic limit (for a discussion of the scaling of W dis with the bath size in a classical set-up, see [32]). Since the expectation of W dis is given by the Kullback-Leibler relative entropy between ̺ τ and ̺ eq Rτ [33][34][35][36], this also means that in the adiabatic limit ̺ τ → ̺ eq…”

Section: Adiabatic Linear Response Of Open Quantum Systemsmentioning

confidence: 99%

Geometric magnetism in open quantum systems

2012

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An isolated classical chaotic system, when driven by the slow change of several parameters, responds with two reaction forces: geometric friction and geometric magnetism. By using the theory of quantum fluctuation relations we show that this holds true also for open quantum systems, and provide explicit expressions for those forces in this case. This extends the concept of Berry curvature to the realm of open quantum systems. We illustrate our findings by calculating the geometric magnetism of a damped charged quantum harmonic oscillator transported along a path in physical space in presence of a magnetic field and a thermal environment. We find that in this case the geometric magnetism is unaffected by the presence of the heat bath.

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Section: Adiabatic Linear Response Of Open Quantum Systemsmentioning

confidence: 99%

Geometric magnetism in open quantum systems

2012

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“…Let us consider the situations in which we make measurements without error and divide the phase-space of the particle into several regions. Then, in each region, a more detailed expression of the Jarzynski equality holds 28 : e ( F −W )/kB T A = P † (A)/P(A), where ··· A is the ensemble average over trajectories under the condition that the particle is observed in region A (A = S or outside S in our set-up) with probability P(A), and P † (A) is the probability that the particle is observed in A under the time-reversed control protocol. Without feedback control, this detailed equality reproduces the Jarzynski equality as e ( F −W )/kB T = A P(A) e ( F −W )/kB T A = A P † (A) = 1.…”

Section: Information Contentmentioning

confidence: 99%

Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality

et al. 2010

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In 1929, Leó Szilárd invented a feedback protocol 1 in which a hypothetical intelligence-dubbed Maxwell's demon-pumps heat from an isothermal environment and transforms it into work. After a long-lasting and intense controversy it was finally clarified that the demon's role does not contradict the second law of thermodynamics, implying that we can, in principle, convert information to free energy 2-6 . An experimental demonstration of this information-to-energy conversion, however, has been elusive. Here we demonstrate that a non-equilibrium feedback manipulation of a Brownian particle on the basis of information about its location achieves a Szilárd-type information-to-energy conversion. Using realtime feedback control, the particle is made to climb up a spiral-staircase-like potential exerted by an electric field and gains free energy larger than the amount of work done on it. This enables us to verify the generalized Jarzynski equality 7 , and suggests a new fundamental principle of an 'information-to-heat engine' that converts information into energy by feedback control.To illustrate the basic idea of our feedback protocol, let us consider a microscopic particle on a spiral-staircase-like potential ( Fig. 1). We set the height of each step comparable to the thermal energy k B T , where k B is the Boltzmann constant and T is temperature. Subjected to thermal fluctuations, the particle jumps between steps stochastically. Although the particle sometimes jumps to an upper step, downward jumps along the gradient are more frequent than upward jumps. In this manner, on average, the particle falls down the stairs unless it is externally pushed up (Fig. 1a). Now, let us consider the following feedback control: We measure the particle's position at regular intervals, and if an upward jump is observed we place a block behind the particle to prevent subsequent downward jumps (Fig. 1b). If this procedure is repeated, the particle is expected to climb up the stairs. Note that, in the ideal case, energy to place the block can be negligible; this implies that the particle can obtain free energy without any direct energy injection. In such a case, what drives the particle to climb up the stairs? This apparent contradiction to the second law of thermodynamics, epitomized by Maxwell's demon, inspired many physicists to generalize the principles of thermodynamics 1,5,6 . It is now understood that the particle is driven by the 'information' gained by the measurement of the particle's location 5,8 .In microscopic systems, thermodynamic quantities such as work, heat and internal energy do not remain constant but particle on a spiral-staircase-like potential with a step height comparable to k B T. The particle stochastically jumps between steps owing to thermal fluctuations. As the downward jumps along the gradient are more frequent than the upward ones, the particle falls down the stairs, on average. b, Feedback control. When an upward jump is observed, a block is placed behind the particle to prevent downward jumps. By repeating ...

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“…The averaged work dissipated when one instantly changes the energies of a system is given by kT times the Kullback-Leibler distance between the initial equilibrium distribution and the final one. This is a special case of the Kawai-ParrondoBrock equality [19,20]. We will make use of this relation all along this article to calculate the work performed at each steps of the process.…”

Section: Measuring the State Of A Two Levels Systemmentioning

confidence: 99%

Thermodynamic cost of measurements

Granger

Kantz

2011

Phys. Rev. E

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The measurement of thermal fluctuations provides information about the microscopic state of a thermodynamic system and can be used in order to extract work from a single heat bath in a suitable cyclic process. We present a minimal framework for the modeling of a measurement device and we propose a protocol for the measurement of thermal fluctuations. In this framework, the measurement of thermal fluctuations naturally leads to the dissipation of work. We illustrate this framework on a simple two states system inspired by the Szilard's information engine.

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Dissipation: The Phase-Space Perspective

Cited by 468 publications

References 14 publications

Geometric magnetism in open quantum systems

Geometric magnetism in open quantum systems

Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality

Thermodynamic cost of measurements

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