Equilibrium distributions in entropy driven balanced processes

For entropy driven balanced processes we obtain final states with Poisson, Bernoulli, negative binomial and P\'olya distributions. We apply this both for complex networks and particle production. For random networks we follow the evolution of the degree distribution, $P_n$, in a system where a node can activate $k$ fixed connections from $K$ possible partnerships among all nodes. The total number of connections, $N$, is also fixed. For particle physics problems $P_n$ is the probability of having $n$ particles (or other quanta) distributed among $k$ states (phase space cells) while altogether a fixed number of $N$ particles reside on $K$ states.Comment: 12 pages no figure

Observables of Lattice Gauge Theory in Minkowski Space

U(1) gauge fields are decomposed into a monopole and photon part across the phase transition from the confinement to the Coulomb phase. We analyze the leading Lyapunov exponents of such gauge field configurations on the lattice which are initialized by quantum Monte Carlo simulations. We observe that the monopole field carries the same Lyapunov exponent as the original U(1) field. Evidence is found that monopole fields stay chaotic in the continuum whereas the photon fields are regular. First results are presented for the full spectrum of Lyapunov exponents of the U(1) gauge system.Comment: Contribution to "QCD02 - High-Energy Physics International Conference in Quantum Chromodynamics" (Montpellier, France, July 02 - 09, 2002); 5 pages, 9 figure

Entropy of expanding QCD matter

Using the lattice QCD equation of state for an isentropically expanding fireball we follow the evolution of the effective number of particles in an ideal gas pV/T. This number reduces roughly to its third around the crossover temperature, which helps to circumvent the entropy obstacle inherent in quark coalescence models of the hadronization.Comment: 5 pages 4 eps figures LaTe

Entropic Distance for Nonlinear Master Equation

More and more works deal with statistical systems far from equilibrium, dominated by unidirectional stochastic processes augmented by rare resets. We analyze the construction of the entropic distance measure appropriate for such dynamics. We demonstrate that a power-like nonlinearity in the state probability in the master equation naturally leads to the Tsallis (Havrda-Charv\'at, Acz\'el-Dar\'oczy) q-entropy formula in the context of seeking for the maximal entropy state at stationarity. A few possible applications of a certain simple and linear master equation to phenomena studied in statistical physics are listed at the end.Comment: Talk given by T.S.Bir\'o at BGL 2017, Gy\"ongy\"os, Hungar

Generating new solutions for relativistic transverse flow at the softest point

Using the method of prolongation we generate new solutions from a simple particular solution for relativistic transverse flow with cylindrical symmetry in 1+3 dimensions. This is an extension of the longitudinal Bjorken flow ansatz and can be applied among others during first order phase transition in an expanding system. The prolongated solution allows for tracing back the flow profile from a transverse flow conjectured at the end of phase transition at CERN SPS heavy ion collisons.Comment: 11 pages LaTeX, 1 ps figur

Gintropy: Gini index based generalization of Entropy

Entropy is being used in physics, mathematics, informatics and in related areas to describe equilibration, dissipation, maximal probability states and optimal compression of information. The Gini index on the other hand is an established measure for social and economical inequalities in a society. In this paper we explore the mathematical similarities and connections in these two quantities and introduce a new measure that is capable to connect these two at an interesting analogy level. This supports the idea that a generalization of the Gibbs--Boltzmann--Shannon entropy, based on a transformation of the Lorenz curve, can properly serve in quantifying different aspects of complexity in socio- and econo-physics.Comment: 13 pages, 3 Figure

Black hole horizons can hide positive heat capacity

Regarding the volume as independent thermodynamic variable we point out that black hole horizons can hide positive heat capacity and specific heat. Such horizons are mechanically marginal, but thermally stable. In the absence of a canonical volume definition, we consider various suggestions scaling differently with the horizon radius. Assuming Euler-homogeneity of the entropy, besides the Hawking temperature, a pressure and a corresponding work term render the equation of state at the horizon thermally stable for any meaningful volume concept that scales larger than the horizon area. When considering also a Stefan--Boltzmann radiation like equation of state at the horizon, only one possible solution emerges: the Christodoulou--Rovelli volume, scaling as $V\sim R^5$, with an entropy $S = \frac{8}{3}S_{BH}$.Comment: 5 pages, no figures, to be published in Phys. Lett.

Analytic solution for relativistic transverse flow at the softest point

We obtain an extension of Bjorken's 1+1 dimensional scaling relativistic flow solution to relativistic transverse velocities with cylindrical symmetry in 1+3 dimensions at constant, homogeneous pressure (vanishing sound velocity). This can be the situation during a first order phase transition converting quark matter into hadron matter in relativistic heavy ion collisions.Comment: 9 pages LaTeX, 1 .eps figure, Figure replaced by another presentation showing contour-lines of QGP-hadron phase mixtures in the longitudinal time - transverse radius plane. To appear in Phys.Lett.

The hadronization line in stringy matter

Using the equation of state of the string model with linear strings comes close to describing the lattice QCD results and offers an explanation for the E/N = 1 GeV hadronization condition found in phenomenological statistical model. The E/N = 6T relation is derived from the zero pressure condition and is a fairly general result. The baryochemical potential dependence of the hadron gas can be met if it is re-interpreted in the framework of an additive quark model.Comment: LaTeX, 7 eps figure