Nonequivalence of the Nernst-Simon and unattainability statements of the third law of thermodynamics

Abstract:The quantum Otto cycle serves as a bridge between the macroscopic world of heat engines and the quantum regime of thermal devices composed from a single element. We compile recent studies of the quantum Otto cycle with a harmonic oscillator as a working medium. This model has the advantage that it is analytically trackable. In addition, an experimental realization has been achieved, employing a single ion in a harmonic trap. The review is embedded in the field of quantum thermodynamics and quantum open systems. The basic principles of the theory are explained by a specific example illuminating the basic definitions of work and heat. The relation between quantum observables and the state of the system is emphasized. The dynamical description of the cycle is based on a completely positive map formulated as a propagator for each stroke of the engine. Explicit solutions for these propagators are described on a vector space of quantum thermodynamical observables. These solutions which employ different assumptions and techniques are compared. The tradeoff between power and efficiency is the focal point of finite-time-thermodynamics. The dynamical model enables the study of finite time cycles limiting time on the adiabatic and the thermalization times. Explicit finite time solutions are found which are frictionless (meaning that no coherence is generated), and are also known as shortcuts to adiabaticity.The transition from frictionless to sudden adiabats is characterized by a non-hermitian degeneracy in the propagator. In addition, the influence of noise on the control is illustrated. These results are used to close the cycles either as engines or as refrigerators. The properties of the limit cycle are described. Methods to optimize the power by controlling the thermalization time are also introduced. At high temperatures, the Novikov-Curzon-Ahlborn efficiency at maximum power is obtained. The sudden limit of the engine which allows finite power at zero cycle time is shown. The refrigerator cycle is described within the frictionless limit, with emphasis on the cooling rate when the cold bath temperature approaches zero.

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“…The second formulation is dynamical, known as the unattainability principle [135,[139][140][141][142]:…”

Section: The Quest To Reach Absolute Zeromentioning

confidence: 99%

The Quantum Harmonic Otto Cycle

Kosloff

Rezek

2017

Entropy

348

362

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“…The Carnot cycle reaching T = 0, which is called the Carnot-Nernst cycle, is possible in case (b) and is also shown in the figure. It should be noted that proofs of equivalence of Nernst principle and Nernst theorem involve a number of additional assumptions [15,16] as illustrated by examples (c), (d), (e) and (f). Cases (c) and (e) indicate that the Nernst principle can be valid while the Nernst theorem is not.…”

Section: Statements Of the Third Lawmentioning

confidence: 99%

“…Cases (d) and (f) demonstrate validity of the Nernst theorem and violation of the Nernst principle. Case (d) considers a special entropy state with S(T, x) = 0 at T > 0 -a system with these properties and Bose-Einstein statistics is discussed by Wheeler [16]. Case (f) implies negative heat capacities due to ∂S/∂T < 0 at T → 0 and x = x 1 .…”

Section: Statements Of the Third Lawmentioning

confidence: 99%

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Teaching the Third Law of Thermodynamics

Klimenko¹

2012

TOTHERJ

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This work gives a brief summary of major formulations of the third law of thermodynamics and their implications, including the impossibility of perpetual motion of the third kind. The last sections of this work review more advanced applications of the third law to systems with negative temperatures and negative heat capacities. The relevance of the third law to protecting the arrow of time in general relativity is also discussed. Additional information, which may useful in analysis of the third law, is given in the Appendices.This short review is written to assist lecturers in selecting a strategy for teaching the third law of thermodynamics to engineering and science students. The paper provides a good summary of the various issues associated with the third law, which are typically scattered over numerous research publications and not discussed in standard textbooks.

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“…It is natural to ask what the bounds are for these quantum devices, and how they compare to the bounds on classical devices. There are many works asking whether quantum systems are bounded by the laws of thermodynamics [20][21][22][23][24][25][26][27] , particularly for systems modeled by Markovian or Bloch-Redfield master equations, see Refs. [20,[28][29][30] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic and quantum bounds on nonlinear dc thermoelectric transport

Whitney

2013

Phys. Rev. B

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I consider the non-equilibrium DC transport of electrons through a quantum system with a thermoelectric response. This system may be any nanostructure or molecule modeled by the nonlinear scattering theory which includes Hartree-like electrostatic interactions exactly, and certain dynamic interaction effects (decoherence and relaxation) phenomenologically. This theory is believed to be a reasonable model when single-electron charging effects are negligible. I derive three fundamental bounds for such quantum systems coupled to multiple macroscopic reservoirs, one of which may be superconducting. These bounds affect nonlinear heating (such as Joule heating), work and entropy production. Two bounds correspond to the first law and second law of thermodynamics in classical physics. The third bound is quantum (wavelength dependent), and is as important as the thermodynamic ones in limiting the capabilities of mesoscopic heat-engines and refrigerators. The quantum bound also leads to Nernst's unattainability principle that the quantum system cannot cool a reservoir to absolute zero in a finite time, although it can get exponentially close.

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Nonequivalence of the Nernst-Simon and unattainability statements of the third law of thermodynamics

Cited by 18 publications

References 2 publications

The Quantum Harmonic Otto Cycle

The Quantum Harmonic Otto Cycle

Teaching the Third Law of Thermodynamics

Thermodynamic and quantum bounds on nonlinear dc thermoelectric transport

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