Theory for non-equilibrium statistical mechanics

This paper reviews a new theory for non-equilibrium statistical mechanics. This gives the non-equilibrium analogue of the Boltzmann probability distribution, and the generalization of entropy to dynamic states. It is shown that this so-called second entropy is maximized in the steady state, in contrast to the rate of production of the conventional entropy, which is not an extremum. The relationships of the new theory to Onsager's regression hypothesis, Prigogine's minimal entropy production theorem, the Langevin equation, the formula of Green and Kubo, the Kawasaki distribution, and the non-equilibrium fluctuation and work theorems, are discussed. The theory is worked through in full detail for the case of steady heat flow down an imposed temperature gradient. A Monte Carlo algorithm based upon the steady state probability density is summarized, and results for the thermal conductivity of a Lennard-Jones fluid are shown to be in agreement with known values. Also discussed is the generalization to non-equilibrium mechanical work, and to non-equilibrium quantum statistical mechanics. As examples of the new theory two general applications are briefly explored: a non-equilibrium version of the second law of thermodynamics, and the origin and evolution of life.     

A high power hybrid mid-IR laser source

An efficient hybrid mid-IR laser system comprising a thulium fibre laser, Ho:YAG solid state laser and a zinc germanium phosphide optical parametric oscillator is presented. A 790 nm diode pumped 1908 nm thulium fibre laser operating at 30 W pumps an RTP q-switched Ho:YAG laser emitting 17 W at 40 kHz and 2090 nm. The zinc germanium phosphide optical parametric oscillator efficiently converts this into the 3-5 μm region producing 10.1 W with 59% optical conversion efficiency and an M² = 1.5.     

Uniqueness,Extinction and Explosivity of Generalised Markov Branching Processes with Pairwise Interaction

We examine basic properties regarding uniqueness, extinction, and explosivity for the generalised Markov branching processes with pairwise interaction. First we establish uniqueness criteria, proving that in the essentially-explosive case the process is honest if and only if the mean death rate is greater than or equal to the mean birth rate, while in the sub-explosive case the process is dishonest only in exceptional circumstances. Explicit expressions are then obtained for the extinction probabilities, the mean extinction times and the conditional mean extinction times. Explosivity is also investigated and an explicit expression for mean explosion time is established.     

Natural time analysis of critical phenomena: The case of acoustic emissions in triaxially deformed Etna basalt

Acoustic emissions exhibit complex correlations between space, time, and magnitude. As such, they present a unique example for a complex time series. We apply the recently introduced method of natural time analysis, which enables the detection of long-range temporal correlations even in the presence of heavy tails and find that the acoustic emissions exhibits features similar to that of other equilibrium or non-equilibrium critical systems such as worldwide seismicity as presented in the Centennial earthquake catalogue which includes global seismicity events with magnitude _Mw>7.0$M_w>7.0$. These results support the universal behaviour of the fracturing processes from the laboratory to the global scale.     

Toward Best Approximation of Nonlinear Systems: A Case of Models with Memory

The problem of nonlinear dynamical system modeling, considered in this paper, is motivated by restrictions arising in real-world tasks. The restrictions are that first, a system input cannot be entirely observed for one trial. Second, the system model must be subjected to the causality principle. Third, the input is corrupted by noise so that no relationship between the reference input and noise is known. Fourth, the model should have some degrees of freedom so that the associated accuracy can be regulated by a variation of these freedom degrees. We propose and justify new procedures for the nonlinear system modeling that are initialized by these motivations. The models are nonlinear and given by so called r-degree operators that can be reduced to a matrix form presentation. To satisfy the restrictions above, the matrices have special structures that we call the lower p-band matrices. The degree r of the models is the required degree of freedom. The rigorous analysis of errors associated with the presented techniques is given. Numerical experiments with real data demonstrate the efficiency of the proposed approach.     

Structural Investigation of New Lithium Amidinates and Guanidinates

A series of potentially useful lithium amidinates and guanidinates were prepared and fully characterized. Treatment of N,N′‐diisopropylcarbodiimide with phenyllithium in diethyl ether afforded the lithium amidinate [PhC(NiPr)₂Li(OEt₂)]₂ ( 1 ). Similar treatment of N,N′‐diorganocarbodiimides R′–N=C=N–R′ [R′ = iPr, cyclohexyl (Cy)] with secondary lithium amides LiNR₂ [R₂ = Et₂, iPr₂, (CH₂)₄] followed by crystallization from THF or 1,4‐dioxane gave the lithium guanidinates [R₂NC(NR′)₂Li(S)]₂ [ 2 : R = Et, R′ = iPr, S = THF; 3 : R₂ = (CH₂)₄, R′ = iPr, S = THF; 4 : R = R′ = iPr, S = ½ 1,4‐dioxane; 5 : R₂ = (CH₂)₄, R′ = Cy, S = 1,4‐dioxane] as crystalline solids. Reaction of N‐lithioaziridine with the corresponding carbodiimides afforded solvent‐deficient [{C₂H₄NC(NiPr₂)₂}₂Li₂(THF)]₂ ( 6 ), and [C₂H₄NC(NEt)(NtBu)Li(THF)]₂ ( 7 ). Crystal structure determination revealed the presence of common ladder‐type dimeric structures for 1 – 5 . Compound 6 exists as a dimer of two ladder‐type dimers in the crystal, and 7 exhibits an unusual dimeric structure comprising an eight‐membered C₂N₄Li₂ ring.     

New Homoleptic Rare‐Earth Metal Complexes Comprising the Unsymmetrically Substituted Amidinate Ligand [MeC(NEt)(NtBu)]–

New homoleptic complexes of selected rare‐earth elements containing the unsymmetrically substituted amidinate ligand [MeC(NEt)(NtBu)]^– [= (L)^–] were synthesized and fully characterized. Treatment of in situ‐prepared Li(L) ( 1 ) with anhydrous lanthanide(III) chlorides, LnCl₃ (Ln = Sc, La, Ce, Ho), afforded three different types of amidinate complexes depending on the ionic radius of the central metal atom. The large La³⁺ formed the octa‐coordinate DME solvate La(L)₃(DME) ( 2 ). Using Ce³⁺, the octa‐coordinate “ate” complex Li(THF)[Ce(L)₄] ( 3 ) was formed. Depending on the crystallization conditions, compound 3 could be crystallized in two modifications differing in the coordination environment around Li. In the case of the smaller Sc³⁺ and Ho³⁺ ions, six‐coordinate homoleptic Sc(L)₃ ( 4 ) and Ho(L)₃ ( 5 ) were isolated. The title compounds were fully characterized by spectroscopic and analytical methods as well as single‐crystal X‐ray diffraction. With Ln = La and Ce, several by‐products incorporating lithium, chlorine and/or oxygen were also isolated and structurally characterized.     

Synthesis of 5-Alkyl- and 5-Phenylamino-Substituted Azothiazole Dyes with Solvatochromic and DNA-Binding Properties

A series of new 5-mono- and 5,5′-bisamino-substituted azothiazole derivatives was synthesized from the readily available diethyl azothiazole-4,4′-dicarboxylate. This reaction most likely comprises an initial Michael-type addition by the respective primary alkyl and aromatic amines at the carbon atom C5 of the substrate. Subsequently, the resulting intermediates are readily oxidized by molecular oxygen to afford the amino-substituted azothiazole derivatives. The latter exhibit remarkably red-shifted absorption bands (λ_abs=507–661 nm) with high molar extinction coefficients and show a strong positive solvatochromism. As revealed by spectrometric titrations and circular and linear dichroism studies, the water-soluble, bis-(dimethylaminopropylamino)-substituted azo dye associates with duplex DNA by formation of aggregates along the phosphate backbone at high ligand–DNA ratios (LDR) and by intercalation at low LDR, which also leads to a significant increase of the otherwise low emission intensity at 671 nm.