A nonequilibrium entropy for dynamical systems

It is proposed to define entropy for nonequilibrium ensembles using a method of coarse graining which partitions phase space into sets which typically have zero measure. These are chosen by considering the totality of future possibilities for observation on the system. It is shown that this entropy is necessarily a nondecreasing function of the timet. There is no contradiction with the reversibility of the laws of motion because this method of coarse graining is asymmetric under time reversal. Under suitable conditions (which are stated explicitly) this entropy approaches the equilibrium entropy ast+ and the fine-grained entropy ast–. In particular, the conditions can always be satisfied if the system is aK-system, as in the Sinai billiard models. Some theorems are given which give information about whether it is possible to generate the partition used here for coarse graining from time translates of a finite partition, and at the same time elucidate the connection between our concept of entropy and the entropy invariant of Kolmogorov and Sinai.Research supported in part by NSF grants PHY78-03816 and PHY78-15920.     

Heat-capacity measurements and thermodynamic functions of crystalline adenine; revised thermodynamic properties of aqueous adenine

The standard molar heat capacity C^°_p,m of adenine(cr) has been measured using adiabatic calorimetry over the range 6<(T/K)<310 and the results used to derive thermodynamic functions for adenine(cr) at smoothed temperatures. At T=298.15 K, C^°_p,m=(142.67±0.29) J · K⁻¹ · mol⁻¹ and the third law entropy S^°_m=(145.62±0.29) J · K⁻¹ · mol⁻¹. The standard molar Gibbs free energy of formation Δ_fG^°_m at T=298.15 K for crystalline adenine was calculated, using the standard molar enthalpy of formation for the compound and entropies of the elements from the literature, and found to be Δ_fG^°_m=(301.4±1.0) kJ · mol⁻¹. The results were combined with solution calorimetry and solubility measurements from the literature to yield revised values for the standard molar thermodynamic properties of aqueous adenine at T=298.15 K: Δ_fG^°_m=(313.4±1.0) kJ · mol⁻¹, Δ_fH^°_m=(129.5±1.4) kJ · mol⁻¹, and S_m^°=(217.68±0.44) J · K⁻¹ · mol⁻¹.     

A Singular Limit Problem for Conservation Laws Related to the Camassa–Holm Shallow Water Equation

We consider a shallow water equation of the Camassa–Holm type, which contains nonlinear dispersive effects as well as fourth order dissipative effects. We prove that as the diffusion and dispersion parameters tend to zero, with a condition on the relative balance between these two parameters, smooth solutions of the shallow water equation converge to discontinuous weak solutions of a scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L ^p setting.     

Is the US stock market becoming weakly efficient over time? Evidence from 80-year-long data

We propose a degree of market efficiency in terms of entropy concepts. The relative efficiency for the US stock market varies over time from 1929 to 2012, with a slight decline in the past 10 years.     

A possible human counterpart of the principle of increasing entropy

It is well-known that the principle of increasing entropy holds for isolated natural systems that contain non-adaptive molecules. Here we present, for the first time, an experimental evidence for a possible human counterpart of the principle in an isolated social system that involves adaptive humans. Our work shows that the human counterpart is valid even though interactions among humans in social systems are distinctly different from those among molecules in natural systems. Thus, it becomes possible to understand social systems from this natural principle, at least to some extent.     

Entropic information for travelling solitons in Lorentz and CPT breaking systems

In this work we group four research topics apparently disconnected, namely solitons, Lorentz symmetry breaking, supersymmetry, and entropy. Following a recent work (Gleiser and Stamatopoulos, 2012), we show that it is possible to construct in the context of travelling wave solutions a configurational entropy measure in functional space, from the field configurations. Thus, we investigate the existence and properties of travelling solitons in Lorentz and CPT breaking scenarios for a class of models with two interacting scalar fields. Here, we obtain a complete set of exact solutions for the model studied which display both double and single-kink configurations. In fact, such models are very important in applications that include Bloch branes, Skyrmions, Yang–Mills, Q-balls, oscillons and various superstring-motivated theories. We find that the so-called Configurational Entropy (CE) for travelling solitons shows that the best value of parameter responsible to break the Lorentz symmetry is one where the energy density is distributed equally around the origin. In this way, the information-theoretical measure of travelling solitons in Lorentz symmetry violation scenarios opens a new window to probe situations where the parameters responsible for breaking the symmetries are arbitrary. In this case, the CE selects the best value of the parameter in the model.     

Crystallization of Pseudopolymorphs of Some Gamboge Pigments. Pyridine,Dimethylformamide and Dimethylsulfoxide Solvates of Morellic Acid,Gambogic Acid and Guttiferic Acid

Abstract

Morellic acid, gambogic acid and guttiferic acid are related naturally-occurring xanthone pigments that yield X-ray quality crystals only from solvents like pyridine, dimethylformamide (dmf) and dimethyl sulfoxide (dmso). The structures of four of these crystals have been determined and are found to contain solvents of crystallization. The solvents hydrogen bond to the carboxyl groups with O—H…O/N motifs previously seen in other carboxylic acids. Distinctive, however, is the presence of an extended though somewhat diffuse array of C—H…O hydrogen bonds that aggregates the entire solute-solvent assemblage in a multi-point manner. Pyridine and dmf are able to mimic each other with respect to their hydrogen bond donating and accepting characteristics and in this respect play equivalent roles in their solvates with morellic acid and gambogic acid. Dmso is seen to self-associate in its guttiferic acid solvate. It is possible that these solvents with multiple hydrogen bonding donor and acceptor capability can act as hydrogen bond nucleators, providing just enough rigidity to the solutes to ensure crystallization.     

A hybrid nanofluid analysis near a parabolic stretched surface

Two dimensional incompressible steady viscous nano-fluid flow with the impacts of heat generation and porous medium is examined numerically. For this objective Ti₆Al₄v are taken as nano-particles dispersed in different base fluids such as methanol, engine oil and water. Basically in this study we will compare three different nano-fluids to assess their flow behaviour and thermal performance. The flow model is developed under certain assumptions. The two dimensional non-linear PDEs are converted into non-linear ODEs with suitable transformation. The numerical procedure is adopted to find the results by using Bvp4c technique in MATLAB. Moreover, graphs are generated for various parameters against the temperature and velocity profiles. The fluid behaviour for different parameter is examined on velocity and temperature profile. It is depicted that for high values of volume fraction and curvature parameter nano-particles leads to high velocity and temperature profile. Moreover, velocity profile decreases for permeability parameter, while temperature profile enhances for heat generation parameter. The influence of Nusselt number and skin friction also assessed. The model of entropy generation is also presented.