Statistical theory of self-similar time series as a nonextensive thermodynamic system

Within Tsallis' nonextensive statistics, a model is elaborated to address self-similar time series as a thermodynamic system. Thermodynamic-type characteristics relevant to temperature, pressure, entropy, internal and free energies are introduced and tested. Stability conditions of time series analysis are discussed in details on the basis of Van der Waals model.Comment: 11 pages, LaTe

Complexity of Self-similar Hierarchical Ensembles

Within the framework of generalized combinatorial approach, the complexity is determined for infinite set of self-similar hierarchical ensembles. This complexity is shown to increase with strengthening of the hierarchy coupling to the value, which decreases with growth of both scattering of this coupling and non-extensivity parameter.Comment: 7 pages, 3 figure

Nonlinear Theory of Stochastic Resonance

Theory of nonlinear resonance, including stochastic one, is developed on the basis of the statistical field theory and using variables action-angle. Explicit expressions of action, proper frequency and nonlinearity parameter as functions of the system energy and the external signal frequency are found for the cases of nonlinear pendulum and double well potential.Comment: 20 pages (LaTeX), 11 figure

Axiomatic theory of nonequilibrium system

Mutually conjugated synergetic schemes are assumed to address evolution of nonequilibrium self-organizing system. Within framework of the former, the system is parameterized by a conserving order parameter being a density, a conjugate field reducing to gradient of related flux, and control parameter, whose driven magnitude fixes stationary state. We show that so-introduced conjugate field and control parameter are relevant to entropy and internal energy, so that self-organization effect is appeared as a negative temperature. Along the line of the conjugated scheme, roles of order parameter, conjugate field and control parameter are played with a flux of conserving value, and gradients of both chemical potential and temperature. With growth of the latter, relevant value of the entropy shows to decrease in supercritical regime related to spontaneous flux-state. We proof that both approach stated on using density and conjugated flux as order parameters follow from unified field theory related to the simplest choice of both Lagrangian and dissipative function.Comment: 10 pages, 2 figures, LaTe

Generalized thermostatistics based on multifractal phase space

We consider the self-similar phase space with reduced fractal dimension $d$ being distributed within domain $0<d<1$ with spectrum $f(d)$. Related thermostatistics is shown to be governed by the Tsallis' formalism of the non-extensive statistics, where role of the non-additivity parameter plays inverted value ${\bar\tau}(q)\equiv 1/\tau(q)>1$ of the multifractal function $\tau(q)= qd(q)-f(d(q))$, being the specific heat, $q\in(1,\infty)$ is multifractal parameter. In this way, the equipartition law is shown to take place. Optimization of the multifractal spectrum $f(d)$ derives the relation between the statistical weight and the system complexity.Comment: 8 pages, LaTe

Self-consistent theory of the long-range order in solid solutions

On the basis of the assumption that atoms play a role of effective Fermions at lattice distribution, the study of the long-range ordering is shown to be reduced to self-consistent consideration of single and collective excitations being relevant to the space distribution of atoms and Fourier transform of such distribution, respectively. A diagram method advanced allows to elaborate complete thermodynamic picture of the long-range ordering of the arbitrary compositional solid solution. The long-range order parameter is found for different chemical potentials of the components to obtain a scope of ordering solid solutions according to relation between degree of the chemical affinity of the components and mixing energy. The boundary composition of the ordering phase AB_n is determined as a function of the chemical potentials of the components and concentrations of impurities and defects. Temperature-compositional dependencies of the order parameter and the sublattice difference of the chemical potentials are determined explicitly. The hydrodynamic behavior of the system is presented by a reactive mode being result of the interference of condensate and fluctuation components of collective excitations. The dispersion law of this mode is displayed experimentally as the Zener peak of the internal friction.Comment: 12 pages, 5 figures, RevTe

Theory of microphase separation of homopolymer-oligomer mixtures

Microphase separated structure consisting of the periodic alternation of the layers of stretched homopolymer chains surrounded by perpendicularly oriented oligomeric tails is studied for both, strongly bonded (ionic) systems and weakly (hydrogen) bonded systems. Our approach is based on the fact that the structure period is determined by alternating associations between the head group of the surfactant and the interacting group of the polymer. Oligomer distribution along the homopolymer chain is described by the effective equation of motion with the segment number playing the role of time. As a result, experimentally observed temperature dependence of the structure period, as well as the dependence of the point of order--disorder transition are determined as functions of the oligomeric fraction.Comment: 4 pages, 5 figures, RevTe

Supersymmetry Theory of Disordered Heteropolymers

The effective motion equation that describes the different monomer alternation along the heteropolymer chain is proposed. On its basis the supersymmetry field scheme that allows to obtain the equations for the structure factor and Green function is built up. The memory and ergodicity breaking effects are investigated depending on the temperature and quenched disorder of the monomer alternation. The phase diagram that determines the existence of the non-ergodic and freezing states is provided.Comment: 13 pages, 7 figures, LaTe

Synergetic theory for jamming transition in traffic flow

The theory of a jamming transition is proposed for the homogeneous car-following model within the framework of Lorenz scheme. We represent a jamming transition as a result of the spontaneous deviations of headway and velocity that is caused by the acceleration/braking rate to be higher than the critical value. The stationary values of headway and velocity deviations, and time of acceleration/braking are derived as functions of control parameter (time needed for car to take the characteristic velocity).Comment: 10 pages, 2 figures, LaTe

Multifractal spectrum of the phase space related to generalized thermostatistics

We consider the set of monofractals within a multifractal related to the phase space being the support of a generalized thermostatistics. The statistical weight exponent $\tau(q)$ is shown to can be modeled by the hyperbolic tangent deformed in accordance with both Tsallis and Kaniadakis exponentials whose using allows one to describe explicitly arbitrary multifractal phase space. The spectrum function $f(d)$, determining the specific number of monofractals with reduced dimension $d$, is proved to increases monotonically from minimum value $f=-1$ at $d=0$ to maximum $f=1$ at $d=1$. The number of monofractals is shown to increase with growth of the phase space volume at small dimensions $d$ and falls down in the limit $d\to 1$.Comment: 10 pages, 6 figure