Creation, Dissipation and Recycling of Resources in Non-Equilibrium Systems

In this article, we define stochastic dynamics for a system coupled to reservoirs. The rules for forward and backward transitions are related by a generalized detailed balance identity involving the system and its reservoirs. We compare the variation of information and of entropy. We define the Carnot dissipation and prove that it can be expressed in terms of cyclic transformations. Lower bounds for partial dissipations are also studied, as well as the effect of switching off certain reservoirs. We also study the near degeneracy of the stochastic matrix, relate it to phase transitions and we show that the reduced dynamics on the set of phases is a permutation. Finally, we relate these concepts to heat, work and more generally to the dissipation and creation of resources, in general systems.     

Fairness in Scheduling

On-line machine scheduling has been studied extensively, but the fundamental issue of fairness in scheduling is still mostly open. In this paper we explore the issue in settings where there are long-lived processes which should be repeatedly scheduled for various tasks throughout the lifetime of a system. For any such instance we develop a notion ofdesiredload of a process, which is a function of the tasks it participates in. Theunfairnessof a system is the maximum, taken over all processes, of the difference between the desired load and the actual load.An example of such a setting is thecarpool problemsuggested by Fagin and Williams [IBM Journal of Research and Development27(2) (1983), 133–139]. In this problem, a set ofnpeople form a carpool. On each day a subset of the people arrive and one of them is designated as the driver. A scheduling rule is required so that the driver will be determined in a “fair” way.We investigate this problem under various assumptions on the input distribution. We also show that the carpool problems can capture several other problems of fairness in scheduling.     

Separation of spiral contacts and the motion of vacuum arcs at highAC currents

A framing camera is used to photograph the vacuum arc between separating spiral-petal vacuum interrupter contacts. The rupture of the molten bridge between the contacts first leads to a high-pressure, transient arc column. This arc motion can become constricted for several milliseconds before it goes diffuse as the current decreases to zero. The current through the spiral contacts produces a magnetic field perpendicular to the arc column, which forces the arc to move outward and run along the periphery of the petals. Several vacuum arc modes occur during the half-cycle of high current arcing. Movies, gap-current curves, and arc voltage traces are used to study the development of the arc motion and how it is affected by the contact structure. This information is used to generate arc appearance diagrams in which the arc form and motion are correlated to instantaneous values of current and gap for a wide range of peak currents. Appearance diagrams are shown for two ranges of opening delay from current onset     

Fluorimetric determination of acidity constants of naphthoic and anthroic acids

A fluorimetric method of determining the acidity constants (pK_a values) of some naphthoic and anthroic acids is presented, based on the changes in fluorescence of solutions of these acids in water on changing the pH. The method is useful in the absence as well as in the presence of excited-state proton transfer. In the latter case, when the excited-state protonation occurs in the same pH region as the ground-state dissociation, resolution of the two processes can be accomplished by addition of a suitable quencher such as iodide. The method permits the accurate determination of the pK_a value of fluorescent compounds, even when they are poorly soluble in water, because of the high sensitivity of the spectrofluorimetry.     

A simple relationship between the hammett acidity function,Ho, and the thermodynamic pKa values of unsubstituted aromatic carboxamides

The well-known failure of the Hammett H_o function to describe the prototropic reaction isotherms of aromatic carboxamides can be corrected by taking account of the hydration requirements of the prototropic reactions of the carboxamides relative to the hydration requirements of the dissociations of the primary amines used as indicators to establish the H_o scale. This approach has been successfully applied to benzamide and the naphthamides. For up to a 4:1 molar ratio of water to sulfuric acid, the amide acidity scale, H_A and the H_o scale are simply related by H_A = H_o — 2 log a_w , where a_w is the activity of water.     

Fluorimetric detection of tautomeric equilibria in 8-aminoquinolines

The 1-methylquinolinium cations derived from 8-aminoquinoline and 8-amino-6-methoxyquinoline were prepared by methylation of the corresponding nitroquinolines and reduction of the nitro-compounds. The dissociation constants of the protonated species of these compounds are almost identical to those of doubly-protonated 8-aminoquinoline and 8-amino-6-methoxyquinoline, respectively, suggesting that the parent quinolines are exclusively first protonated at the ring nitrogen atom. However, the molar absorptivities of the 1-methyl derivatives at their longest-wavelength absorption maxima are substantially greater than the corresponding absorptivities of the unmethylated aminoquinolines, a result which suggests tautomerism of the singly-protonated parent quinolines, with a proportion of the population protonated at the amino group. Fluorescence spectroscopy reveals a single emission from the 8-amino-6-methoxy-1-methylquinolinium ion and two excitation-wavelength-dependent fluorescences from the 8-amino-6-methoxyquinolinium ion, confirming the occurrence of tautomerism and supporting choice of the absorptiometric approach rather than the titrimetric approach as the preferred method for the detection of tautomerism and the calculation of tautomeric equilibrium constants.     

The tautomerism of Omeprazole in solution: a 1H and 13C NMR study

The tautomerism of 5(6)-methoxy-2-([(4-methoxy-3,5-dimethyl-2-pyridinyl)methyl] sulfinyl)-1H-benzimidazole (omeprazole) was determined in solution, K(T) = 0.59 in THF at 195 K, in favor of the 6-methoxy tautomer. The assignment of the signals was made by comparison with its two N-methyl derivatives in acetone-d6 and through theoretical calculations of the absolute shieldings (GIAO/DFT/6-311++G**).     

Statistical mechanics of a dynamical system based on Conway's game of Life

We study a discrete dynamical system whose evolution is governed by rules similar to those of Conway's game of Life but also include a stochastic element (parametrized by a temperature). Statistical properties that are examined are density as a function of temperature and entropy (suitably defined). A phase transition and a certain thermodynamic constant of the motion are observed.Lady Davis Visiting Scientist at the Technion 1974–75.     

Thermodynamic arrow for a mixing system

The purpose of this paper is to study the appearance of time asymmetry in dynamical systems. The systems are harmonic oscillators and a certain mixing flow on the torus. The asymmetry is a kind of frictional force, but we emphasize that the boundary conditions, a usual source of asymmetry in studies of this sort, are taken to be time symmetric. For the mixing flow the response of the system, as reflected in its entropy as a function of time, occurs only subsequent to the friction, while for the oscillators the effects are both before and after. Some general discussion also takes up the question of which of the foregoing systems is a better model of the physical world for purposes of correlating arrows of time.Work supported in part by U.S. Army Research Office (Durham, N.C.).