Quantum bath refrigeration towards absolute zero: unattainability principle challenged

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 third-law formulation known as the unattainability principle

Entropy and Its Quantum Thermodynamical Implication for Anomalous Spectral Systems

The state function entropy and its quantum thermodynamical implication for two typical dissipative systems with anomalous spectral densities are studied by investigating on their low-temperature quantum behavior. In all cases it is found that the entropy decays quickly and vanishes as the temperature approaches zero. This reveals a good conformity with the third law of thermodynamics and provides another evidence for the validity of fundamental thermodynamical laws in the quantum dissipative region.Comment: 10 pages, 3 figure

Transient energy excitation in shortcuts to adiabaticity for the time dependent harmonic oscillator

There is recently a surge of interest to cut down the time it takes to change the state of a quantum system adiabatically. We study for the time-dependent harmonic oscillator the transient energy excitation in speed-up processes designed to reproduce the initial populations at some predetermined final frequency and time, providing lower bounds and examples. Implications for the limits imposed to the process times and for the principle of unattainability of the absolute zero, in a single expansion or in quantum refrigerator cycles, are drawn.Comment: 7 pages, 6 figure

Universal restrictions to the conversion of heat into work derived from the analysis of the Nernst theorem as a uniform limit

We revisit the relationship between the Nernst theorem and the Kelvin-Planck statement of the second law. We propose that the exchange of entropy uniformly vanishes as the temperature goes to zero. The analysis of this assumption shows that is equivalent to the fact that the compensation of a Carnot engine scales with the absorbed heat so that the Nernst theorem should be embedded in the statement of the second law. ----- Se analiza la relaci{\'o}n entre el teorema de Nernst y el enunciado de Kelvin-Planck del segundo principio de la termodin{\'a}mica. Se{\~n}alamos el hecho de que el cambio de entrop{\'\i}a tiende uniformemente a cero cuando la temperatura tiende a cero. El an{\'a}lisis de esta hip{\'o}tesis muestra que es equivalente al hecho de que la compensaci{\'o}n de una m{\'a}quina de Carnot escala con el calor absorbido del foco caliente, de forma que el teorema de Nernst puede derivarse del enunciado del segundo principio.Comment: 8pp, 4 ff. Original in english. Also available translation into spanish. Twocolumn format. RevTe

Spacetime and vacuum as seen from Moscow

An extended text of the talk given at the conference ``2001: A Spacetime Odyssey'', to be published in the Proceedings of the Inaugural Conference of the Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, 21-25 May 2001, M.J. Duff and J.T. Liu eds., World Scientific, Singapore, 2002; and of Historical Lecture ``Vacuum as seen from Moscow'' at the CERN Summer School, 10 August, 2001. Contents: Introduction; Pomeranchuk on vacuum; Landau on parity, P, and combined parity, CP; Search and discovery of $K_L^0 \to \pi^+ \pi^-$; "Mirror world"; Zeldovich and cosmological term; QCD vacuum condensates; Sakharov and baryonic asymmetry of the universe, BAU; Kirzhnits and phase transitions; Vacuum domain walls; Monopoles, strings, instantons, and sphalerons; False vacuum; Inflation; Brane and Bulk; Acknowledgments; References.Comment: 17 pages, 2 figure

Electronic thermal transport in strongly correlated multilayered nanostructures

The formalism for a linear-response many-body treatment of the electronic contributions to thermal transport is developed for multilayered nanostructures. By properly determining the local heat-current operator, it is possible to show that the Jonson-Mahan theorem for the bulk can be extended to inhomogeneous problems, so the various thermal-transport coefficient integrands are related by powers of frequency (including all effects of vertex corrections when appropriate). We illustrate how to use this formalism by showing how it applies to measurements of the Peltier effect, the Seebeck effect, and the thermal conductance.Comment: 17 pages, 4 figures, submitted to Phys. Rev.

Notes on the Third Law of Thermodynamics.I

We analyze some aspects of the third law of thermodynamics. We first review both the entropic version (N) and the unattainability version (U) and the relation occurring between them. Then, we heuristically interpret (N) as a continuity boundary condition for thermodynamics at the boundary T=0 of the thermodynamic domain. On a rigorous mathematical footing, we discuss the third law both in Carath\'eodory's approach and in Gibbs' one. Carath\'eodory's approach is fundamental in order to understand the nature of the surface T=0. In fact, in this approach, under suitable mathematical conditions, T=0 appears as a leaf of the foliation of the thermodynamic manifold associated with the non-singular integrable Pfaffian form $\delta Q_{rev}$. Being a leaf, it cannot intersect any other leaf $S=$ const. of the foliation. We show that (N) is equivalent to the requirement that T=0 is a leaf. In Gibbs' approach, the peculiar nature of T=0 appears to be less evident because the existence of the entropy is a postulate; nevertheless, it is still possible to conclude that the lowest value of the entropy has to belong to the boundary of the convex set where the function is defined.Comment: 29 pages, 2 figures; RevTex fil

Diffuse-Charge Dynamics in Electrochemical Systems

The response of a model micro-electrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem consists of a symmetric binary electrolyte between parallel-plate, blocking electrodes which suddenly apply a voltage. Compact Stern layers on the electrodes are also taken into account. The Nernst-Planck-Poisson equations are first linearized and solved by Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The ``weakly nonlinear'' limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter $\epsilon = \lambda_D/L$, where $\lambda_D$ is the screening length and $L$ the electrode separation. At leading order, the system initially behaves like an RC circuit with a response time of $\lambda_D L / D$ (not $\lambda_D^2/D$), where $D$ is the ionic diffusivity, but nonlinearity violates this common picture and introduce multiple time scales. The charging process slows down, and neutral-salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale, $L^2/D$. In the ``strongly nonlinear'' regime (controlled by a dimensionless parameter resembling the Dukhin number), this effect produces bulk concentration gradients, and, at very large voltages, transient space charge. The article concludes with an overview of more general situations involving surface conduction, multi-component electrolytes, and Faradaic processes.Comment: 10 figs, 26 pages (double-column), 141 reference

Quantum vacuum fluctuations

The existence of irreducible field fluctuations in vacuum is an important prediction of quantum theory. These fluctuations have many observable consequences, like the Casimir effect which is now measured with good accuracy and agreement with theory, provided that the latter accounts for differences between real experiments and the ideal situation considered by Casimir. But the vacuum energy density calculated by adding field mode energies is much larger than the density observed around us through gravitational phenomena. This ``vacuum catastrophe'' is one of the unsolved problems at the interface between quantum theory on one hand, inertial and gravitational phenomena on the other hand. It is however possible to put properly formulated questions in the vicinity of this paradox. These questions are directly connected to observable effects bearing upon the principle of relativity of motion in quantum vacuum.Comment: 8 pages, 2 figures, contribution to a special issue in CRAS (Comptes rendus de l'Academie des Sciences), corrected typos, added reference

Water seepage beneath dams on soluble evaporite deposits: a laboratory and field study (Caspe Dam, Spain)

The paper presents analytical methods and results for assessing the variation in the concentration of sulphate (and other ions) over space and time in groundwater flowing through a soluble evaporite terrain beneath a dam. The influence of effective porosity, groundwater flow velocity and the specific rate of dissolution (K′) are considered. The theoretical analysis was tested in a scale model simulating a dam constructed on heavily karstified bedrock. A simple and useful method for assessing how much material is lost through dissolution and how the rate of dissolution changes over time is considered in the context of the Caspe Dam, Spain