abstract

The complexity (or simplicity) of a system can be characterized through very many paths. A quite interesting and operational one, which we follow here, consists in making use of entropic concepts. The thermodynamical and statistical-mechanical foundations of this approach, as well as its (analytical, computational, observational, and experimental) applications for natural, artificial and social systems will be briefly reviewed.

abstract

Quasi-power law ensembles are discussed from the perspective of nonextensive Tsallis distributions characterized by a nonextensive parameter \(q\). A number of possible sources of such distributions are presented in more detail. It is further demonstrated that the data suggest that nonextensive parameters deduced from Tsallis distributions functions \(f\left (p_\mathrm {T}\right )\), \(q_1\), and from multiplicity distributions (connected with Tsallis entropy), \(q_2\), are not identical and that they are connected via \(q_1 + q_2 = 2\). It is also shown that Tsallis distributions can be obtained directly from Shannon information entropy, provided some special constraints are imposed. They are connected with the type of dynamical processes under consideration (additive or multiplicative). Finally, it is shown how a Tsallis distribution can accommodate the log-oscillating behavior apparently seen in some multiparticle data.

abstract

An unstable fixed point of a map cannot be calculated by iteration from almost any initial value. If such a map is concave, it is possible to turn it convex by reforming the map. An unstable fixed point is thereby made stable for iteration. The technique of reformation is presented with examples from the physics and math literature.

abstract

The time evolution of the density fluctuation of a two-dimensional high-density ultrarelativistic-like electron gas is studied at the long wavelength and zero temperature limits. The model we consider is a reduced version of the relativistic Sawada model within the massless Dirac particles frame. Time correlation functions are exactly calculated through the recurrence relations method, and a dynamic equivalence between the ultrarelativistic-like and the nonrelativistic dense electron gas systems is stated by the present approach.

abstract

In this work, we use the ideas of scaling to investigate stochastic process for asymptotic times, we play particular attention to the phenomenon of anomalous diffusion. The combination of method of complex variables with scaling concepts allows us to investigate the mechanism of diffusion as well for intermediates times. We generalized the concept of the diffusion exponent to include other than the asymptotic power-law behaviour. A method is proposed to obtain the diffusion coefficient analytically through the introduction of a time scaling factor \(\lambda \). We obtain also an exact expression for \(\lambda \) for all kinds of diffusion. Moreover, we show that \(\lambda \) is a universal parameter determined by the diffusion exponent. The results are then compared with numerical calculations and very good agreement is observed. We show the existence of two kinds of ballistic diffusion, one ergodic and another non-ergodic. The method is general and may be applied to many types of stochastic problem.

abstract

We derive a Fluctuation-Dissipation Theorem (FDT) from the generalized Langevin equation for both the equilibrium and far-from-equilibrium states. The equilibrium FDT is obtained under the assumption of energy balance and stationarity condition. We derive a non-equilibrium relation of the FDT, which can be applied in slow relaxation processes and non-ergodic systems whenever the second law of thermodynamics is brought to bear. We obtain also a relationship between stationary and non-ergodic behaviour based on the non-equilibrium FDT. Emphasis is placed on ballistic diffusion, which goes to local equilibrium.

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This contribution gives a short introduction into the theory of anomalous diffusion and relaxation with illustrations from computer simulations of biomolecular systems. The theory is presented from the perspective of the non-equilibrium statistical physics, confronting stochastic models with exact results which have been recently obtained on the basis of asymptotic analysis. In this context, conditions for anomalous diffusion will be discussed and the Kubo relations for the fractional diffusion and relaxation constant will be derived.

abstract

The giant unicellular slime mould Physarum polycephalum forms an extended network of stands (veins) that provide for an effective intracellular transportation system, which coarsens in time. The network coarsening was investigated numerically using an agent-based model and the results were compared to experimental observations. The coarsening process of both numerical and experimental networks was characterised by analyses of the kinetics of coarsening, of the distributions of geometric network parameters (as, for instance, the lengths and widths of vein segments) and of network topologies.

abstract

By means of contact-density chain growth simulations, we compare thermodynamic properties of adsorption at solid substrates for two lattice polymers with 32 and 128 monomers, which gives insight into finite-size effects governing the compact phases. In both cases, we construct the entire structural phase diagrams parametrized by temperature and solvent quality, and investigate the fluctuations of macroscopic thermodynamic quantities that enable us to distinguish structural phases and to locate transition regions.

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In this work, we extend the etching model [B.A. Mello, A. Chaves, F.A. Oliveira, Phys. Rev. E 63, 041113 (2001)] to \(d+1\) dimensions. This permits us to investigate its exponents behaviour on higher dimensions, to try to verify the existence of an upper critical dimension for the KPZ equations. Our results show that \(d=4\) is not an upper critical dimension for the etching model, and suggest that if an upper critical dimension exists it must larger than six.

abstract

The properties of the Mott insulator to superfluid phase transition are obtained through the fermionic approximation in the Jaynes–Cummings–Hubbard model on linear, square, SC, FCC, and BCC Bravais lattices, for varying excitation number and atom-cavity frequency detuning. We find that the Mott lobes and the critical hopping are not scalable only for the FCC lattice. At the large excitation number regime, the critical hopping is scalable for all the lattices and it does not depend on the detuning.

abstract

We address the question regarding the effect of correlated random spring constants in the one-dimensional harmonic model. We consider all masses to be equal but the spring constants given by a random sequence with long-range correlations. We generate the long-range correlated sequence of spring constants by using a fractional Brownian motion with a power-law spectral density \(S(k)=1/k^{\alpha }\). Using an exact diagonalization formalism, we compute the participation moments of eigenmodes within the band of allowed frequencies. We unveil a regime on which all modes below a critical frequency become extended.