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Th. M. Nieuwenhuizen - One of the best experts on this subject based on the ideXlab platform.
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Thermodynamics and small quantum systems
Journal of Modern Optics, 2003Co-Authors: Th. M. NieuwenhuizenAbstract:Abstract Small quantum systems non-weakly coupled to a bath become in the quantum regime surrounded by a cloud of photons or phonons, which modifies their thermodynamic behaviour. Exactly solvable examples are the Brownian motion of a quantum particle in a harmonic confining potential and coupled to a harmonic quantum thermal bath, e.g. an ion in a Penning trap, and a spin immersed in a bosonic bath, as occurs in NMR physics. It appears that the Clausius Inequality d Q≤TdS can be violated. For non-adiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Experimental set-ups for testing some of the effects are discussed.
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Thermodynamics and small quantum systems
Journal of Modern Optics, 2003Co-Authors: Th. M. NieuwenhuizenAbstract:Small quantum systems non-weakly coupled to a bath become in the quantum regime surrounded by a cloud of photons or phonons, which modifies their thermodynamic behavior. Exactly solvable examples are the Brownian motion of a quantum particle in a harmonic confining potential and coupled to a harmonic quantum thermal bath, e.g. an ion in a Penning trap, and a spin immersed in a bosonic bath, as occurs in NMR physics. It appears that the Clausius Inequality $\dbarrm Q\le T\d S$ can be violated. For non-adiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Experimental setups for testing some of the effects are discussed.
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On testing the violation of the Clausius Inequality in nanoscale electric circuits
Physical Review B, 2002Co-Authors: Armen E. Allahverdyan, Th. M. NieuwenhuizenAbstract:The Clausius Inequality, one of the classical formulations of the second law, was recently found to be violated in the quantum regime. Here this result is formulated in the context of a mesoscopic or nanoscale linear RLC circuit interacting with a thermal bath. Previous experiments in this and related fields are analyzed and possibilities of experimental detection of the violation are pointed out. It is discussed that recent experiments reached the range of temperatures, where the effect should be visible, and that a part of the proposal was already confirmed.
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Reply on Comment on ``Extraction of work from a single thermal bath in the quantum regime''
arXiv: Statistical Mechanics, 2000Co-Authors: Armen E. Allahverdyan, Th. M. NieuwenhuizenAbstract:In our recent letter [1] we discussed that thermodynamics is violated in quantum Brownian motion beyond the weak coupling limit. In his comment, Tasaki [2] derives an Inequality for the relative entropy and claims, without making any dynamical assumption, that the Clausius Inequality is valid, thus contradicting our statements [1]. Here we point out that the claim is unfunded, since the author did not properly identify the concept of heat. Tasaki also applies the Inequality to Thomson's formulation of the second law. This application is invalid as well, since the author did not correctly identify the concept of work. Therefore, Tasaki's Inequality is perfectly compatible with our findings.
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extraction of work from a single thermal bath in the quantum regime
Physical Review Letters, 2000Co-Authors: Armen E. Allahverdyan, Th. M. NieuwenhuizenAbstract:The stationary state of a quantum particle strongly coupled to a quantum thermal bath is known to be non-Gibbsian, due to entanglement with the bath. For harmonic potentials, where the system can be described by effective temperatures, thermodynamic relations are shown to take a generalized Gibbsian form that may violate the Clausius Inequality. For the weakly anharmonic case, a Fokker-Planck-type description is constructed. It is shown that then work can be extracted from the bath by cyclic variation of a parameter. These apparent violations of the second law are the consequence of quantum coherence in the presence of the slightly off-equilibrium nature of the bath.
Armen E. Allahverdyan - One of the best experts on this subject based on the ideXlab platform.
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Thomson's formulation of the second law for macroscopic and finite work sources
Entropy, 2004Co-Authors: Armen E. Allahverdyan, Roger Balian, Theodorus Maria NieuwenhuizenAbstract:Thomson's formulation of the second law states: no work can be extracted from an equilibrium system through a cyclic process. A simple, general proof is presented for the case of macroscopic sources of work. Next the setup is generalized towards situations, where the corresponding work-source is not macroscopic. It is shown that using such a source one can extract energy from an equilibrium system by means of a cyclic process. However, this extraction is accompanied by an entropy increase of the source, in a manner resembling the Clausius Inequality.
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On testing the violation of the Clausius Inequality in nanoscale electric circuits
Physical Review B, 2002Co-Authors: Armen E. Allahverdyan, Th. M. NieuwenhuizenAbstract:The Clausius Inequality, one of the classical formulations of the second law, was recently found to be violated in the quantum regime. Here this result is formulated in the context of a mesoscopic or nanoscale linear RLC circuit interacting with a thermal bath. Previous experiments in this and related fields are analyzed and possibilities of experimental detection of the violation are pointed out. It is discussed that recent experiments reached the range of temperatures, where the effect should be visible, and that a part of the proposal was already confirmed.
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Bath generated work extraction in two‐level systems
AIP Conference Proceedings, 2002Co-Authors: Claudia Pombo, Armen E. Allahverdyan, Theo M. NieuwenhuizenAbstract:The spin‐boson model, often used in NMR and ESR physics, quantum optics and spin‐tronics, is considered in a solvable limit to model a spin one‐half particle interacting with a bosonic thermal bath. By applying external pulses to a non‐equilibrium initial state of the spin, work can be extracted from the thermalized bath. It occurs on the timescale T2 inherent to transversal (‘quantum’) fluctuations. The work (partly) arises from heat given off by the surrounding bath, while the spin entropy remains constant during a pulse. This presents a violation of the Clausius Inequality and the Thomson formulation of the second law (cycles cost work) for the two‐level system.
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Reply on Comment on ``Extraction of work from a single thermal bath in the quantum regime''
arXiv: Statistical Mechanics, 2000Co-Authors: Armen E. Allahverdyan, Th. M. NieuwenhuizenAbstract:In our recent letter [1] we discussed that thermodynamics is violated in quantum Brownian motion beyond the weak coupling limit. In his comment, Tasaki [2] derives an Inequality for the relative entropy and claims, without making any dynamical assumption, that the Clausius Inequality is valid, thus contradicting our statements [1]. Here we point out that the claim is unfunded, since the author did not properly identify the concept of heat. Tasaki also applies the Inequality to Thomson's formulation of the second law. This application is invalid as well, since the author did not correctly identify the concept of work. Therefore, Tasaki's Inequality is perfectly compatible with our findings.
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extraction of work from a single thermal bath in the quantum regime
Physical Review Letters, 2000Co-Authors: Armen E. Allahverdyan, Th. M. NieuwenhuizenAbstract:The stationary state of a quantum particle strongly coupled to a quantum thermal bath is known to be non-Gibbsian, due to entanglement with the bath. For harmonic potentials, where the system can be described by effective temperatures, thermodynamic relations are shown to take a generalized Gibbsian form that may violate the Clausius Inequality. For the weakly anharmonic case, a Fokker-Planck-type description is constructed. It is shown that then work can be extracted from the bath by cyclic variation of a parameter. These apparent violations of the second law are the consequence of quantum coherence in the presence of the slightly off-equilibrium nature of the bath.
Claudio Maggi - One of the best experts on this subject based on the ideXlab platform.
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Erratum: Heat, temperature and Clausius Inequality in a model for active Brownian particles
Scientific Reports, 2018Co-Authors: Umberto Marini Bettolo Marconi, Andrea Puglisi, Claudio MaggiAbstract:Scientific Reports 7: Article number: 46496; published online: 21 April 2017; updated: 08 June 2018 The original version of this Article contained an error in the Accepted date ‘17 March 2017’ which was incorrectly given as ‘17 March 2015’. This error has now been corrected in the PDF and HTML versions of the Article.
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Erratum: Heat, temperature and Clausius Inequality in a model for active Brownian particles.
Scientific reports, 2018Co-Authors: Umberto Marini Bettolo Marconi, Andrea Puglisi, Claudio MaggiAbstract:This corrects the article DOI: 10.1038/srep46496.
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Heat, temperature and Clausius Inequality in a model for active Brownian particles
Scientific Reports, 2017Co-Authors: Umberto Marini Bettolo Marconi, Andrea Puglisi, Claudio MaggiAbstract:Methods of stochastic thermodynamics and hydrodynamics are applied to a recently introduced model of active particles. The model consists of an overdamped particle subject to Gaussian coloured noise. Inspired by stochastic thermodynamics, we derive from the system’s Fokker-Planck equation the average exchanges of heat and work with the active bath and the associated entropy production. We show that a Clausius Inequality holds, with the local (non-uniform) temperature of the active bath replacing the uniform temperature usually encountered in equilibrium systems. Furthermore, by restricting the dynamical space to the first velocity moments of the local distribution function we derive a hydrodynamic description where local pressure, kinetic temperature and internal heat fluxes appear and are consistent with the previous thermodynamic analysis. The procedure also shows under which conditions one obtains the unified coloured noise approximation (UCNA): such an approximation neglects the fast relaxation to the active bath and therefore yields detailed balance and zero entropy production. In the last part, by using multiple time-scale analysis, we provide a constructive method (alternative to UCNA) to determine the solution of the Kramers equation and go beyond the detailed balance condition determining negative entropy production.
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Heat, temperature and Clausius Inequality in a model for active brownian particles
Scientific reports, 2017Co-Authors: Umberto Marconi, Andrea Puglisi, Claudio MaggiAbstract:Methods of stochastic thermodynamics and hydrodynamics are applied to the a recently introduced model of active particles. The model consists of an overdamped particle subject to Gaussian coloured noise. Inspired by stochastic thermodynamics, we derive from the system's Fokker-Planck equation the average exchanges of heat and work with the active bath and the associated entropy production. We show that a Clausius Inequality holds, with the local (non-uniform) temperature of the active bath replacing the uniform temperature usually encountered in equilibrium systems. Furthermore, by restricting the dynamical space to the first velocity moments of the local distribution function we derive a hydrodynamic description where local pressure, kinetic temperature and internal heat fluxes appear and are consistent with the previous thermodynamic analysis. The procedure also shows under which conditions one obtains the unified coloured noise approximation (UCNA): such an approximation neglects the fast relaxation to the active bath and therefore yields detailed balance and zero entropy production. In the last part, by using multiple time-scale analysis, we provide a constructive method (alternative to UCNA) to determine the solution of the Kramers equation and go beyond the detailed balance condition determining negative entropy production.
Eric Lutz - One of the best experts on this subject based on the ideXlab platform.
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Experimental verification of a reversed Clausius Inequality in an isolated system
arXiv: Quantum Gases, 2020Co-Authors: Daniel Mayer, Eric Lutz, Artur WideraAbstract:The second law of thermodynamics is a fundamental law of Nature. It is almost universally associated with the Clausius Inequality that lower bounds a change in entropy by the ratio of supplied heat and temperature. However, this result presupposes that a system is in contact with a heat bath that drives it to a thermal state. For isolated systems that are moved from an initial equilibrium state by a dissipative heat exchange, the Clausius Inequality has been predicted to be reversed. We here experimentally investigate the nonequilibrium thermodynamics of an isolated dilute gas of ultracold Cesium atoms that can be either thermalized or pushed out of equilibrium by means of laser cooling techniques. We determine in both cases the phase-space dynamics by tracing the evolution of the gas with position-resolved fluorescence imaging, from which we evaluate all relevant thermodynamic quantities. Our results confirm the validity of the usual Clausius Inequality for the first process and of the reversed Clausius Inequality for the second transformation.
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Generalized Clausius Inequality for nonequilibrium quantum processes.
Physical review letters, 2010Co-Authors: Sebastian Deffner, Eric LutzAbstract:We show that the nonequilibrium entropy production for a driven quantum system is larger than the Bures length, the geometric distance between its actual state and the corresponding equilibrium state. This universal lower bound generalizes the Clausius Inequality to arbitrary nonequilibrium processes beyond linear response. We further derive a fundamental upper bound for the quantum entropy production rate and discuss its connection to the Bremermann-Bekenstein bound.
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System-bath entanglement in quantum thermodynamics
Physical Review A, 2009Co-Authors: Stefanie Hilt, Eric LutzAbstract:We consider a quantum harmonic oscillator linearly coupled to a bath of harmonic oscillators and evaluate the degree of entanglement between system and bath using the negativity as an exact entanglement measure. We establish the existence of a critical temperature above which the system-bath negativity vanishes. Our results imply that system-bath entanglement is not responsible for the violation of the Clausius Inequality observed in the low-temperature\char21{}strong-coupling regime [Phys. Rev. Lett. 85, 1799 (2000)], as the latter still occurs well above the critical temperature.
S.e. Wright - One of the best experts on this subject based on the ideXlab platform.
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A generalized and explicit conceptual statement of the principle of the second law of thermodynamics
International Journal of Engineering Science, 2017Co-Authors: S.e. WrightAbstract:Abstract The Clausius Inequality, the fundamental statement of the second law of thermodynamics, focuses on the net entropy rejection by heat transfer out of a closed system operating in a cyclic manner. Recently, the Clausius Inequality was re-stated to correctly apply to systems regardless of the form of heat transfer, and in particular systems with radiative transfer. This is important for many engineering systems because all matter emits thermal radiation continuously due to non-zero temperature. Other statements of the second law also generally refer to heat transfer and heat engines. Of even greater importance, the focus is on equilibrium processes and relations, whereas actual engineering systems are overwhelmingly non-equilibrium by nature. Although not explicitly stated in the Clausius Inequality, the second law principle encompasses the universal approach to obtain uniformity or equilibrium, a state of maximum entropy or disorder. By nature this approach to equilibrium is through non-equilibrium processes that continuously produce entropy as they occur. This paper attempts to capture a more generalized conceptual statement of the second law, that explicitly states various aspects of the second law principle for the purposes of engineering education; a statement that applies to any scenario, system or process.
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The Clausius Inequality corrected for heat transfer involving radiation
International Journal of Engineering Science, 2007Co-Authors: S.e. WrightAbstract:Abstract The objective of this paper is to prove that the Clausius Inequality must be re-stated to have general applicability for heat transfer involving radiative fluxes. The integrand (đQ/T) of the Clausius expression applies to heat conduction and convection, but does not hold for most radiative transfer scenarios, with the exception of reversible infinitesimal net blackbody radiation transfer. In other cases involving radiative transfer, the equality holds for a cycle even though irreversible heat addition by radiative transfer occurs. This is without the erroneous presumption of entropy destruction anywhere in the cycle. Thus, the Clausius Inequality indicates reversibility for a cycle that includes an irreversible process. Further, in some radiative cases the quantity đQ/T, where T is the boundary temperature, is not the entropy transfer at the system boundary, and in fact, primarily represents entropy production within the system. It is also clear that in another case considered, the quantity đQ/T had no physical meaning whatsoever. Consequently, the Clausius expression has been re-stated so that it is applicable to cycles with processes involving any form of heat transfer. A new integrand (đQcc/T + đSNet,Rad) is presented, allowing the Clausius Inequality to generally apply to all heat transfer scenarios. The work in this paper emphasizes the need to re-state other fundamental equations allowing applicability to all heat transfer processes, and draws attention to the unique character of radiative entropy calculations.
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On the entropy of radiative heat transfer in engineering thermodynamics
International Journal of Engineering Science, 2001Co-Authors: S.e. Wright, David Scott, J. B. Haddow, Marc A. RosenAbstract:The objective of this paper is to improve the understanding and also to simplify the calculation of the entropy transferred by thermal radiation (TR). Many thermodynamic texts incorrectly imply that the entropy flux of TR is the same as that for heat conduction, the heat flux divided by the local temperature (q/T). Also, fundamental equations, such as those derived from the Clausius Inequality, express the entropy flux of TR in a q/T type form. However, for blackbody radiation (BR) emission a 4/3 factor is present and in this paper it is shown that the entropy flux of non-blackbody radiation (NBR) emission is even farther removed from q/T. The misuse of the heat conduction entropy flux equation for TR emission causes the irreversibility of a device to be underestimated whether the surface of the device is hot or cold relative to its surroundings. Further, it is shown that the reversible form of the Clausius expression applies when TR is involved yet the expression for irreversible processes does not apply. Finally, simple approximate expressions for the entropy of gray radiation (GR) are presented, as the exclusive use of numerical integration is laborious.