Quantum Refrigerator and the III-law of Thermodynamics (original) (raw)

Quantum refrigerators and the third law of thermodynamics

Physical Review E, 2012

The rate of temperature decrease of a cooled quantum bath is studied as its temperature is reduced to absolute zero. The third law of thermodynamics is then quantified dynamically by evaluating the characteristic exponent ζ of the cooling process dT (t) dt ∼ −T ζ when approaching absolute zero, T → 0. A continuous model of a quantum refrigerator is employed consisting of a working medium composed either by two coupled harmonic oscillators or two coupled two-level systems. The refrigerator is a nonlinear device merging three currents from three heat baths: a cold bath to be cooled, a hot bath as an entropy sink, and a driving bath which is the source of cooling power. A heat-driven refrigerator (absorption refrigerator) is compared to a power-driven refrigerator. When optimized, both cases lead to the same exponent ζ , showing a lack of dependence on the form of the working medium and the characteristics of the drivers. The characteristic exponent is therefore determined by the properties of the cold reservoir and its interaction with the system. Two generic heat bath models are considered: a bath composed of harmonic oscillators and a bath composed of ideal Bose/Fermi gas. The restrictions on the interaction Hamiltonian imposed by the third law are discussed. In the Appendices, the theory of periodically driven open systems and its implication for thermodynamics are outlined.

quantum refrigerators and the iii-law of thermodynamics

Quantum thermodynamics addresses the emergence of thermodynamical laws from quantum mechanics. The III-law of thermodynamics has been mostly ignored. There are seemingly two independent formulation of the third law of thermodynamics, both originally stated by Nernst. The first is known as Nernst heat theorem, which is purely static, and implies that the entropy flow from any substance at the absolute zero is zero. And the second formulation known as the unattainability principle practically state that no refrigerator can cool a system to absolute zero at finite time. We explore the dynamic version which is the vanishing of rate of temperature decrease of a cooled quantum bath when T → 0. The III-law is then quantified dynamically by evaluating the characteristic exponent ξ of the cooling process:

Quantum thermodynamic cooling cycle

2001

The quantum-mechanical and thermodynamic properties of a 3-level molecular cooling cycle are derived. An inadequacy of earlier models is rectified in accounting for the spontaneous emission and absorption associated with the coupling to the coherent driving field via an environmental reservoir.

Quantum refrigerator in the quest for the absolute zero temperature

2008

One of the formulations of the third laws of thermodynamics is that a processes become more isentropic as one approaches the absolute zero temperatures. We examine this prediction by studying an operating model of a quantum refrigerator pumping heat from a cold to a hot reservoir. The working medium consists of a gas of noninteracting harmonic oscillators. The model can be solved in closed form in the quasi-static limit or numerically for general conditions. It is found that the isentropic limit for Tc --> 0 is approached only on the expansion segment of the refrigeration cycle. The scaling of the cooling rate with temperature is shown to be consistent with the second law of thermodynamics. This scaling is also consistent with the unattainability principle which is an alternative formulation of the third law of thermodynamics.

Quantum heat engines and refrigerators: continuous devices

Annual review of physical chemistry, 2014

Quantum thermodynamics supplies a consistent description of quantum heat engines and refrigerators up to a single few-level system coupled to the environment. Once the environment is split into three (a hot, cold, and work reservoir), a heat engine can operate. The device converts the positive gain into power, with the gain obtained from population inversion between the components of the device. Reversing the operation transforms the device into a quantum refrigerator. The quantum tricycle, a device connected by three external leads to three heat reservoirs, is used as a template for engines and refrigerators. The equation of motion for the heat currents and power can be derived from first principles. Only a global description of the coupling of the device to the reservoirs is consistent with the first and second laws of thermodynamics. Optimization of the devices leads to a balanced set of parameters in which the couplings to the three reservoirs are of the same order and the exter...

The quantum refrigerator: The quest for absolute zero

Europhysics Letters (epl), 2009

The scaling of the optimal cooling power of a reciprocating quantum refrigerator is sought as a function of the cold bath temperature as T c → 0. The working medium consists of noninteracting particles in a harmonic potential. Two closed-form solutions of the refrigeration cycle are analyzed, and compared to a numerical optimization scheme, focusing on cooling toward zero temperature.

Quantum refrigerators in quest of the absolute zero

Journal of Applied Physics, 2000

The second and third laws of thermodynamics can be used to establish a fundamental bound for the maximum possible cooling rate in approaching the absolute zero of temperature. In modeling the behavior of the molecular refrigerators geared toward attaining ultralow temperatures, only quantum mechanical, as opposed to classical physics, models can be admissible. As a simple model, we analyze a three-level quantum refrigerator, and in particular its irreversible thermodynamic performance as absolute zero is approached.

Optimal Performance of Quantum Refrigerators

2009

A reciprocating quantum refrigerator is studied with the purpose of determining the limitations of cooling to absolute zero. We find that if the energy spectrum of the working medium possesses an uncontrollable gap, then there is a minimum achievable temperature above zero. Such a gap, combined with a negligible amount of noise, prevents adiabatic following during the demagnetization stage which is the necessary condition for reaching T c → 0. The refrigerator is based on an Otto cycle where the working medium is an interacting spin system with an energy gap. For this system the external control Hamiltonian does not commute with the internal interaction. As a result during the demagnetization and magnetization segments of the operating cycle the system cannot follow adiabatically the temporal change in the energy levels. We connect the nonadiabatic dynamics to quantum friction. An adiabatic measure is defined characterizing the rate of change of the Hamiltonian. Closed form solutions are found for a constant adiabatic measure for all the cycle segments. We have identified a family of quantized frictionless cycles with increasing cycle times. These cycles minimize the entropy production. Such frictionless cycles are able to cool to T c = 0. External noise on the controls eliminates these frictionless cycles. The influence of phase and amplitude noise on the demagnetization and magnetization segments is explicitly derived. An extensive numerical study of optimal cooling cycles was carried out which showed that at sufficiently low temperature the noise always dominated restricting the minimum temperature.

The Quantum Absorption Refrigerator

2011

A quantum absorption refrigerator driven by noise is studied with the purpose of determining the limitations of cooling to absolute zero. The model consists of a working medium coupled simultaneously to hot, cold and noise baths. Explicit expressions for the cooling power are obtained for Gaussian and Poisson white noise. The quantum model is consistent with the first and second laws of thermodynamics. The third law is quantified, the cooling power J c vanishes as J c ∝ T α c , when T c → 0, where α = d + 1 for dissipation by emission and absorption of quanta described by a linear coupling to a thermal bosonic field, where d is the dimension of the bath.

Quantum Bath Refrigeration towards Absolute Zero: Challenging the Unattainability Principle

Physical Review Letters, 2012

A minimal model of a quantum refrigerator (QR), i.e. a periodically phase-flipped two-level system permanently coupled to a finite-capacity bath (cold bath) and an infinite heat dump (hot bath), is introduced and used to investigate the cooling of the cold bath towards the absolute zero (T = 0). Remarkably, the temperature scaling of the cold-bath cooling rate reveals that it does not vanish as T → 0 for certain realistic quantized baths, e.g. phonons in strongly disordered media (fractons) or quantized spin-waves in ferromagnets (magnons). This result challenges Nernst's thirdlaw formulation known as the unattainability principle.