Thermodynamics of a subensemble of a canonical ensemble

Two approaches to describe the thermodynamics of a subsystem that interacts with a thermal bath are considered. Within the first approach, the mean system energy $E_{S}$ is identified with the expectation value of the system Hamiltonian, which is evaluated with respect to the overall (system+bath) equilibrium distribution. Within the second approach, the system partition function $Z_{S}$ is considered as the fundamental quantity, which is postulated to be the ratio of the overall (system+bath) and the bath partition functions, and the standard thermodynamic relation $E_{S}=-d(\ln Z_{S})/d\beta$ is used to obtain the mean system energy. % ($\beta\equiv 1/(k_{B}T)$, $k_{B}$ is the Boltzmann constant, %and $T$ is the temperature). Employing both classical and quantum mechanical treatments, the advantages and shortcomings of the two approaches are analyzed in detail for various different systems. It is shown that already within classical mechanics both approaches predict significantly different results for thermodynamic quantities provided the system-bath interaction is not bilinear or the system of interest consists of more than a single particle. Based on the results, it is concluded that the first approach is superior

Self-similarity of single-channel transmission for electron transport in nanowires

We demonstrate that the single-channel transmission in the resonance tunneling regime exhibits self-similarity as a function of the nanowire length and the energy of incident electrons. The self-similarity is used to design the nonlinear transformation of the nanowire length and energy which, on the basis of known values of transmission for a certain region on the energy-length plane, yields transmissions for other regions on this plane. Test calculations with a one-dimensional tight-binding model illustrate the described transformations. Density function theory based transport calculations of Na atomic wires confirm the existence of the self-similarity in the transmission

What can be learned about molecular reorientation from single molecule polarization microscopy?

We have developed a general approach for the calculation of the single molecule polarization correlation function C(t), which delivers a correlation of the emission dichroisms at time 0 and t. The approach is model independent and valid for general asymmetric top molecules. The key dynamic quantities of our analysis are the even-rank orientational correlation functions, the weighted sum of which yields C(t). We have demonstrated that the use of non-orthogonal schemes for the detection of the single molecule polarization responses makes it possible to manipulate the weighting coefficients in the expansion of C(t). Thus valuable information about the orientational correlation functions of the rank higher than second can be extracted from C(t)

Angular momentum dependent friction slows down rotational relaxation under non-equilibrium conditions

It has recently been shown that relaxation of the rotational energy of hot non-equlibrium photofragments (i) slows down significantly with the increase of their initial rotational temperature and (ii) differs dramatically from the relaxation of the equilibrium rotational energy correlation function, manifesting thereby breakdown of the linear response description [Science 311, 1907 (2006)]. We demonstrate that this phenomenon may be caused by the angular momentum dependence of rotational friction. We have developed the generalized Fokker-Planck equation whose rotational friction depends upon angular momentum algebraically. The calculated rotational correlation functions correspond well to their counterparts obtained via molecular dynamics simulations in a broad range of initial non-equilibrium conditions. It is suggested that the angular momentum dependence of friction should be taken into account while describing rotational relaxation far from equilibrium

Manifestation of nonequilibrium initial conditions in molecular rotation: the generalized J-diffusion model

In order to adequately describe molecular rotation far from equilibrium, we have generalized the J-diffusion model by allowing the rotational relaxation rate to be angular momentum dependent. The calculated nonequilibrium rotational correlation functions (CFs) are shown to decay much slower than their equilibrium counterparts, and orientational CFs of hot molecules exhibit coherent behavior, which persists for several rotational periods. As distinct from the results of standard theories, rotational and orientational CFs are found to dependent strongly on the nonequilibrium preparation of the molecular ensemble. We predict the Arrhenius energy dependence of rotational relaxation times and violation of the Hubbard relations for orientational relaxation times. The standard and generalized J-diffusion models are shown to be almost indistinguishable under equilibrium conditions. Far from equilibrium, their predictions may differ dramatically

Gradual Internal Reforming of Ethanol in Solid Oxide Fuel cells

AbstractElectrolyte (yttria-stabilised zirconia, YSZ) supported solid oxide fuel cells (SOFCs) were fabricated using spin coating of standard LSM cathode and Ni-YSZ cermet anode. A ceria-based catalytic layer was deposited onto the anode with a special current collector design. Such a single cell configuration allows operation by gradual internal reforming of direct carbon-containing fuels. First, the fabricated single cells were operated with hydrogen to determine the optimised conditions of fuel concentration and flow rate regarding faradaïc efficiency. Then, the fuel was switched to dry ethanol and the cells were operated for several hours (100h) with good stability. Post-operation electron microcopy analyses revealed no carbon formation in the anode layer. The results indicate that the gradual internal reforming mechanism is effective, opening up the way to multi-fuel SOFCs, provided that a suitable catalyst layer and cell design are available

Effects of Three Months of Low Molecular Weight Heparin (dalteparin) Treatment After Bypass Surgery for Lower Limb Ischemia—A Randomised Placebo-controlled Double Blind Multicentre Trial

AbstractObjectivesTo test the hypothesis that long-term postoperative dalteparin (Fragmin®, Pharmacia Corp) treatment improves primary patency of peripheral arterial bypass grafts (PABG) in lower limb ischemia patients on acetylsalicylic acid (ASA) treatment.DesignProspective randomised double blind multicenter study.Materials and methodsUsing a computer algorithm 284 patients with lower limb ischemia, most with pre-operative ischemic ulceration or partial gangrene, from 12 hospitals were randomised, after PABG, to 5000IU dalteparin or placebo injections once daily for 3 months. All patients received 75mg of ASA daily for 12 months. Graft patency was assessed at 1, 3 and 12 months.ResultsAt 1 year, 42 patients had died or were lost to follow-up. Compliance with the injection schedule was 80%. Primary patency rate, in the dalteparin versus the control group, respectively, was 83 versus 80% (n.s.) at 3 months and 59% for both groups at 12 months. Major complication rates and cardiovascular morbidity were not different between the two groups.ConclusionsIn patients on ASA treatment, long-term postoperative dalteparin treatment did not improve patency after peripheral artery bypass grafting. Therefore, low molecular weight heparin treatment cannot be recommended for routine use after bypass surgery for critical lower limb ischemia

A unified approach to the derivation of work theorems for equilibrium and steady-state, classical and quantum Hamiltonian systems

We present a unified and simple method for deriving work theorems for classical and quantum Hamiltonian systems, both under equilibrium conditions and in a steady state. Throughout the paper, we adopt the partitioning of the total Hamiltonian into the system part, the bath part, and their coupling. We rederive many equalities which are available in the literature and obtain a number of new equalities for nonequilibrium classical and quantum systems. Our results can be useful for determining partition functions and (generalized) free energies through simulations and/or measurements performed on nonequilibrium systems