Quantum thermodynamic Carnot and Otto-like cycles for a two-level system

From the thermodynamic equilibrium properties of a two-level system with variable energy-level gap $\Delta$, and a careful distinction between the Gibbs relation $dE = T dS + (E/\Delta) d\Delta$ and the energy balance equation $dE = \delta Q^\leftarrow - \delta W^\to$, we infer some important aspects of the second law of thermodynamics and, contrary to a recent suggestion based on the analysis of an Otto-like thermodynamic cycle between two values of $\Delta$ of a spin-1/2 system, we show that a quantum thermodynamic Carnot cycle, with the celebrated optimal efficiency $1 - (T_{low}/T_{high})$, is possible in principle with no need of an infinite number of infinitesimal processes, provided we cycle smoothly over at least three (in general four) values of $\Delta$, and we change $\Delta$ not only along the isoentropics, but also along the isotherms, e.g., by use of the recently suggested maser-laser tandem technique. We derive general bounds to the net-work to high-temperature-heat ratio for a Carnot cycle and for the 'inscribed' Otto-like cycle, and represent these cycles on useful thermodynamic diagrams.Comment: RevTex4, 4 pages, 1 figur

A nonlinear model dynamics for closed-system, constrained, maximal-entropy-generation relaxation by energy redistribution

We discuss a nonlinear model for the relaxation by energy redistribution within an isolated, closed system composed of non-interacting identical particles with energy levels e_i with i=1,2,...,N. The time-dependent occupation probabilities p_i(t) are assumed to obey the nonlinear rate equations tau dp_i/dt=-p_i ln p_i+ alpha(t)p_i-beta(t)e_ip_i where alpha(t) and beta(t) are functionals of the p_i(t)'s that maintain invariant the mean energy E=sum_i e_ip_i(t) and the normalization condition 1=sum_i p_i(t). The entropy S(t)=-k sum_i p_i(t) ln p_i(t) is a non-decreasing function of time until the initially nonzero occupation probabilities reach a Boltzmann-like canonical distribution over the occupied energy eigenstates. Initially zero occupation probabilities, instead, remain zero at all times. The solutions p_i(t) of the rate equations are unique and well-defined for arbitrary initial conditions p_i(0) and for all times. Existence and uniqueness both forward and backward in time allows the reconstruction of the primordial lowest entropy state. The time evolution is at all times along the local direction of steepest entropy ascent or, equivalently, of maximal entropy generation. These rate equations have the same mathematical structure and basic features of the nonlinear dynamical equation proposed in a series of papers ended with G.P.Beretta, Found.Phys., 17, 365 (1987) and recently rediscovered in S. Gheorghiu-Svirschevski, Phys.Rev.A, 63, 022105 and 054102 (2001). Numerical results illustrate the features of the dynamics and the differences with the rate equations recently considered for the same problem in M.Lemanska and Z.Jaeger, Physica D, 170, 72 (2002).Comment: 11 pages, 7 eps figures (psfrag use removed), uses subeqn, minor revisions, accepted for Physical Review

Optimization of material distributions in fast breeder reactors

"MIT-4105-6."Based on a Sc. D. thesis submitted by C.P. Tzanos to the Dept. of Nuclear Engineering, 1971Includes bibliographical references (pages 188-190)AT(30-1)-410

The smallest refrigerators can reach maximal efficiency

We investigate whether size imposes a fundamental constraint on the efficiency of small thermal machines. We analyse in detail a model of a small self-contained refrigerator consisting of three qubits. We show analytically that this system can reach the Carnot efficiency, thus demonstrating that there exists no complementarity between size and efficiency.Comment: 9 pages, 1 figure. v2: published versio

Axiomatic relation between thermodynamic and information-theoretic entropies

Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a measure of uncertainty. In this Letter, we connect these two notions of entropy, using an axiomatic framework for thermodynamics [Lieb, Yngvason, Proc. Roy. Soc.(2013)]. In particular, we obtain a direct relation between the Clausius entropy and the Shannon entropy, or its generalisation to quantum systems, the von Neumann entropy. More generally, we find that entropy measures relevant in non-equilibrium thermodynamics correspond to entropies used in one-shot information theory

A quantum solution to the arrow-of-time dilemma

The arrow of time dilemma: the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e. entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened. This situation is completely indistinguishable from their not having happened at all. In the light of this observation, the second law of thermodynamics is reduced to a mere tautology: physics cannot study those processes where entropy has decreased, even if they were commonplace.Comment: Contains slightly more material than the published version (the additional material is clearly labeled in the latex source). Because of PRL's title policy, the leading "A" was left out of the title in the published pape

Applied thermionic research Quarterly progress report, 4 Mar. - 4 Jun. 1968

Oxidation products of cesium studied by differential thermal analysi

Plasma Electronics

Contains research objectives and reports on six research objectives.National Science Foundation (Grant G-24073)Lincoln Laboratory, Purchase Order DDL BB-107U. S. Air Force under Contract AF 19(628)-50

Plasma Dynamics

Contains reports on three research projects.United States Atomic Energy Commission (Contract AT(30-1)-1842)United States Air Force, Air Force Cambridge Research Center, Air Research and Development Command (Contract AF19(604)-5992)National Science Foundation (Grant G-9330)Flight Accessories Laboratory, Wright-Patterson Air Force Base (WADD Contract AF33(616)-3984