Search Results (7)

The objective of this study is to model astrophysical systems using the nonlinear Fokker–Planck equation, with the Adomian method chosen for its iterative and precise solutions in this context, applying boundary conditions relevant to data from the Rossi X-ray Timing Explorer (RXTE). The results include analysis of 156 X-ray intensity distributions from X-ray binaries (XRBs), exhibiting long-tail profiles consistent with Tsallis q-Gaussian distributions. The corresponding q-values align with the principles of Tsallis thermostatistics. Various diffusion hypotheses—classical, linear, nonlinear, and anomalous—are examined, with q-values further supporting Tsallis thermostatistics. Adjustments in the parameter α (related to the order of fractional temporal derivation) reveal the extent of the memory effect, strongly correlating with fractal properties in the diffusive process. Extending this research to other XRBs is both possible and recommended to generalize the characteristics of X-ray scattering and electromagnetic waves at different frequencies originating from similar astronomical objects. Full article

A study was undertaken to investigate the effects of small boron additions on the solidification and microstructure of hypo-eutectic alloyed grey cast iron. The characteristic temperatures upon crystallisation of the treated metal melt were recorded, specifically those concerning small boron addition by using thermal analysis with the ATAS system. Additionally, a standardised wedge test was set to observe any changes in chill performance. The microstructures of thermal analysis samples were analysed using a light optical microscope (LOM) and field emission scanning electron microscopy (FE-SEM) equipped with energy dispersive spectroscopy (EDS), which reveal variations in graphite count number with the addition of boron within observed random and undercooled flake graphite. The effect of boron was estimated by the classical analytical and statistical approach. The solidification behaviour under equilibrium conditions was predicted by a thermodynamic approach using Thermo-Calc. Based on all gathered data, a response model was set with boron for given melt quality and melt treatment using the experimentally determined data. The study reveals that boron as a ferrite and carbide-promoting element under the experimental set shows weak nucleation potential in synergy with other heterogenic nuclei at increased solidification rates, but no considerable changes were observed by the TA samples solidified at slower cooling rates, indicating the loss of the overall inoculation effect. The potential presence of boron nitride as an inoculator for graphite precipitation for a given melt composition and melt treatment was not confirmed in this study. It seems that boron at increased solidification rates can contribute to overall inoculation, but at slower cooling rates these effects are gradually lost. In the last solidification range, an increased boron content could have a carbide forming nature, as is usually expected. The study suggests that boron in traces could affect the microstructure and properties of hypo-eutectic alloyed grey cast iron. Full article

We review and show the connection between three different theories proposed for the thermodynamic treatment of systems not obeying the additivity ansatz of classical thermodynamics. In the 1950s, Landsberg proposed that when a system comes into contact with a heat bath, its energy levels are redistributed. Based on this idea, he produced an extended thermostatistical framework that accounts for unknown interactions with the environment. A decade later, Hill devised his celebrated nanothermodynamics, where he introduced the concept of subdivision potential, a new thermodynamic variable that accounts for the vanishing additivity of increasingly smaller systems. More recently, a thermostatistical framework at strong coupling has been formulated to account for the presence of the environment through a Hamiltonian of mean force. We show that this modified Hamiltonian yields a temperature-dependent energy landscape as earlier suggested by Landsberg, and it provides a thermostatistical foundation for the subdivision potential, which is the cornerstone of Hill’s nanothermodynamics. Full article

Non-Newtonian calculus naturally unifies various ideas that have occurred over the years in the field of generalized thermostatistics, or in the borderland between classical and quantum information theory. The formalism, being very general, is as simple as the calculus we know from undergraduate courses of mathematics. Its theoretical potential is huge, and yet it remains unknown or unappreciated. Full article

We numerically study the first-principle dynamics and thermostatistics of a d-dimensional classical inertial Heisenberg ferromagnetic model ( $d=1,2,3$ ) with interactions decaying with the distance $r_{ij}$ as $1/r_{ij}^{\alpha }$ ( $\alpha \ge 0$ ), where the limit $\alpha =0$ ( $\alpha \to \infty$ ) corresponds to infinite-range (nearest-neighbour) interactions, and the ratio $\alpha /d>1$ ( $0\le \alpha /d\le 1$ ) characterizes the short-ranged (long-ranged) regime. By means of first-principle molecular dynamics we study: (i) The scaling with the system size $\mathcal{N}$ of the maximum Lyapunov exponent $\lambda$ in the form $\lambda \sim {\mathcal{N}}^{-\kappa }$ , where $\kappa (\alpha /d)$ depends only on the ratio $\alpha /d$ ; (ii) The time-averaged single-particle angular momenta probability distributions for a typical case in the long-range regime $0\le \alpha /d\le 1$ (which turns out to be well fitted by q-Gaussians), and (iii) The time-averaged single-particle energies probability distributions for a typical case in the long-range regime $0\le \alpha /d\le 1$ (which turns out to be well fitted by q-exponentials). Through the Lyapunov exponents we observe an intriguing, and possibly size-dependent, persistence of the non-Boltzmannian behavior even in the $\alpha /d>1$ regime. The universality that we observe for the probability distributions with regard to the ratio $\alpha /d$ makes this model similar to the $\alpha$ -XY and $\alpha$ -Fermi-Pasta-Ulam Hamiltonian models as well as to asymptotically scale-invariant growing networks. Full article

Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the N-body phase space with the given total energy. Due to Boltzmann's principle, e^S=tr(δ(E-H)), its geometrical size is related to the entropy S(E,N,...). This definition does not invoke any information theory, no thermodynamic limit, no extensivity, and no homogeneity assumption, as are needed in conventional (canonical) thermo-statistics. Therefore, it describes the equilibrium statistics of extensive as well of non-extensive systems. Due to this fact it is the fundamental definition of any classical equilibrium statistics. It can address nuclei and astrophysical objects as well. All kind of phase transitions can be distinguished sharply and uniquely for even small systems. It is further shown that the second law is a natural consequence of the statistical nature of thermodynamics which describes all systems with the same -- redundant -- set of few control parameters simultaneously. It has nothing to do with the thermodynamic limit. It even works in systems which are by far than any thermodynamic "limit". Full article

We calculate the phase space volume Ω occupied by a nonextensive system of N classical particles described by an equilibrium (or steady-state, or long-term stationary state of a nonequilibrium system) distribution function, which slightly deviates from Maxwell-Boltzmann (MB) distribution in the high energy tail. We explicitly require that the number of accessible microstates does not change respect to the extensive MB case. We also derive, within a classical scheme, an analytical expression of the elementary cell that can be seen as a macrocell, different from the third power of Planck constant. Thermodynamic quantities like entropy, chemical potential and free energy of a classical ideal gas, depending on elementary cell, are evaluated. Considering the fractional deviation from MB distribution we can deduce a physical meaning of the nonextensive parameter q of the Tsallis nonextensive thermostatistics in terms of particle correlation functions (valid at least in the case, discussed in this work, of small deviations from MB standard case). Full article