The Quantum Absorption Refrigerator (1109.0728v2)

Abstract: 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 proportional to T_c^{alpha}, when T_c approach 0, where alpha =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.

The Quantum Absorption Refrigerator

The paper entitled "The Quantum Absorption Refrigerator" by Amikam Levy and Ronnie Kosloff provides an intricate examination of a novel quantum absorption refrigeration model driven by noise. The research primarily explores the theoretical limitations on cooling as the absolute zero temperature is approached, offering valuable insights into the scaling behavior, as dictated by thermodynamic laws, particularly the third law of thermodynamics. This paper merges concepts from quantum thermodynamics with practical implications in quantum refrigeration systems, extending the theoretical foundations established in prior studies.

Quantum Thermodynamics and Refrigeration

The authors conceptualize the refrigerator using a working medium that interfaces simultaneously with hot, cold, and noisy reservoirs. A fundamental aspect of this model is the consistency with thermodynamic laws, specifically applying the first and second laws to affirm energy conservation and positive entropy production. The third law is examined through the behavior of the cooling power, $\mathcal{J}_c$, as it diminishes according to $\mathcal{J}_c \propto T_c^{\alpha}$ when $T_c \rightarrow 0$. Here, $\alpha$ is identified as $d+1$, where $d$ represents the dimension of the bath coupled to the system, highlighting the complexity introduced by quantum interactions.

Theoretical Framework and Equations

The refrigerator model is constructed using a Hamiltonian framework involving three interacting oscillators, each interacting with different reservoirs. Using Heisenberg equations for open systems, the model incorporates dissipative superoperators to capture thermodynamic interactions precisely. Gaussian and Poisson noise sources are investigated as replacements for the conventional work reservoir—each with distinct implications on the refrigeration cycle.

Gaussian Noise: In the Gaussian noise model, the stochastic field is described by zero mean and delta-time correlation, simplifying the derivation of the Master equation. The cooling power is expressed with a coefficient of performance (COP), restricted by the Carnot cycle, grounded in the system’s oscillator dynamics.

Poisson Noise: The Poisson noise model introduces impulses that dynamically transfer energy between oscillators in contact with hot and cold baths. Using impulse distributions, the effective noise parameter and energy shift are calculated. This model is elaborately pictured, with entropy production as a regular function of impulse strength.

Key Numerical Results

The paper meticulously derives quantitative expressions for cooling power under both Gaussian and Poisson noise conditions. Significant attention is paid to steady-state solutions that facilitate calculating heat currents and optimizing scale functions—demonstrating both conformity to thermodynamic laws and the intricate dependency on noise parameters.

Implications and Future Directions

The exploration of quantum absorption refrigerators unveils critical limitations in cooling processes governed by quantum dynamics. The analysis underscores the potential of autonomous quantum devices over externally driven variants for reliable scaling and efficiency. Future developments in quantum thermodynamic systems may focus on refining noise sources, optimizing control parameters for minimized entropy production, and enhancing the COP of quantum refrigerators. This research contributes a substantial theoretical foundation for advancing quantum cooling technologies and inspiring further inquiry into efficient quantum thermodynamic appliances.