Thermostatistical analysis for short-range interaction potentials

In this paper, we study the thermodynamics of short-range central potentials, namely, the Lee–Wick (LW) potential, and the Plasma potential. In the first part of the paper, we obtain the numerical solution for the orbits equation for these potentials. Posteriorly, we introduce the thermodynamics through the microcanonical and canonical ensembles formalism defined on the phase space of the system. We calculate the density of states associated with the LW and the Plasma potentials. From density of states, we obtain the thermodynamical physical quantities like entropy and temperature as functions of the energy. We also use the Boltzmann–Gibbs formalism to obtain the partition functions, the mean energy and the thermal capacity for these short-range potentials.

Effects of Hadron-Quark Phase Transitions in Hybrid Stars within the NJL Model

We study local and non-local Polyakov Nambu-Jona-Lasinio models and analyze their respective phase transition diagram. We construct hybrid stars using the zero temperature limit of the local and non-local versions of Nambu-Jona-Lasinio model for quark matter and the modern GM1(L) parametrization of the non-linear relativistic mean field model for hadronic matter. We compare our models with data from PSR J1614-2230 and PSR J0343+0432 and also from GW170817 and its electromagnetic counterpart GRB170817A and AT2017gfo. We study observational signatures of the appearance of a mixed phase as a result of modeling a phase transition that mimics the Gibbs formalism and compare the results with the sharp first-order phase transition obtained using the Maxwell construction. We also study in detail the g-mode associated with discontinuities in the equation of state, and calculate non-radial oscillation modes using relativistic Cowling approximation.

Vapour-liquid phase transition and metastability

The paper deals with the modelling of the relaxation processes towards thermodynamic equilibrium in a liquid-vapour isothermal mixture. Focusing on the van der Waals equation of state, we construct a constrained optimization problem using Gibbs' formalism and characterize all possible equilibria: coexistence states, pure phases and metastable states. Coupling with time evolution, we develop a dynamical system whose equilibria coincide with the minimizers of the optimization problem. Eventually we consider the coupling with hydrodynamics and use the dynamical system as a relaxation source terms in an Euler-type system. Numerical results illustrate the ability of the whole model to depict coexistence and metastable states as well.

A thermodynamically consistent model of a liquid-vapor fluid with a gas

This work is devoted to the consistent modeling of a three-phase mixture of a gas, a liquid and its vapor. Since the gas and the vapor are miscible, the mixture is subjected to a non-symmetric constraint on the volume. Adopting the Gibbs formalism, the study of the extensive equilibrium entropy of the system allows to recover the Dalton’s law between the two gaseous phases. In addition, we distinguish whether phase transition occurs or not between the liquid and its vapor. The thermodynamical equilibria are described both in extensive and intensive variables. In the latter case, we focus on the geometrical properties of equilibrium entropy. The consistent characterization of the thermodynamics of the three-phase mixture is used to introduce two Homogeneous Equilibrium Models (HEM) depending on mass transfer is taking into account or not. Hyperbolicity is investigated while analyzing the entropy structure of the systems. Finally we propose two Homogeneous Relaxation Models (HRM) for the three-phase mixtures with and without phase transition. Supplementary equations on mass, volume and energy fractions are considered with appropriate source terms which model the relaxation towards the thermodynamical equilibrium, in agreement with entropy growth criterion.

Admissible equations of state for immiscible and miscible mixtures

This paper addresses the construction of admissible Equations of State (EoS) for compressible two-phase ows. We investigate two approaches. In the first one, the mixture is treated as a single uid with a complex thermodynamic. Most of the time the available EoS are determined experimentally and are often incomplete EoS, i.e. we know only the pressure as a function of the volume and the temperature. We present here a general framework to compute a complete EoS based on such an incomplete EoS. In the second approach, each phase is depicted by its own EoS. Following the Gibbs formalism, the mixture entropy is the sum of the phasic entropies which achieves its maximum at equilibrium. Depending on the miscibility of the mixture, one gets different geometrical properties on the resulting mixture entropy. Eventually we address the coupling of mixture EoS with the dynamic of the uid. Homogeneous Equilibrium and Relaxation Models (HEM and HRM) are introduced for an immiscible and a miscible two-phase mixture. Hyperbolicity is ensured taking advantage of the concavity properties of the mixture entropies.

ON THE NATURE AND DYNAMICS OF THE SEISMOGENETIC SYSTEM OF SOUTH CALIFORNIA, USA: AN ANALYSIS BASED ON NON-EXTENSIVE STATISTICAL PHYSICS

We examine the nature of the seismogenetic system in South California, USA, by searching for evidence of non-extensivity in the earthquake record. We attempt to determine whether earthquakes are generated by a self-excited Poisson process, in which case they obey Boltzmann-Gibbs thermodynamics, or by a Critical process, in which long-range interactions in non-equilibrium statesare expected (correlation) and the thermodynamics deviate from the Boltzmann-Gibbs formalism. Emphasis is given to background earthquakes since it is generally agreed that aftershock sequences comprise correlated sets. Accordingly, the analysis is based on the accurate earthquake catalogue compiled of the South California Earthquake Data Center, in which aftershocks are either included or have been removed with a stochastic declustering procedure. We examine multivariate cumulative frequency distributions of earthquake magnitudes, interevent time and interevent distance, in the context of Non-Extensive Statistical Physics, which is a generalization of extensive Boltzmann-Gibbs thermodynamics to non-equilibrating (non-extensive) systems. The results indicate a persistent subextensive seismogenetic system exhibiting long-range, moderate to high correlation. Criticality appears to be a plausible causative mechanism although conclusions cannot be drawn until alternative complexity mechanisms can be ruled out.

Specific Heat of Square Spin Ice in Finite Point Ising-Like Dipoles Model

In the model of finite number (up to 24) of point Ising-like magnetic dipoles with magnetostatic interaction on square 2D lattice within the framework of statistical physics, with using Gibbs formalism and by the means of Metropolis algorithm the heating dependence of temperature has been evaluated. The temperature dependence of the heat capacity on finite number of point dipoles has the finite value of maximum. Together with increase of the system in size the heating peak grows and moves to the area with higher temperature. The obtained results are useful in experimental verification of statistical models, as well as in development and testing of approximate calculation methods of systems with great number of particles.

Interfacial energy states of moisture-exposed cracks in mica

Results of crack growth observations on mica in water-containing environments are described. The study focuses on equilibrium crack states for reversed loading cycles, i.e., for initial propagation through virgin solid and subsequent retraction-repropagation through healed or misoriented-healed interfaces. Departures from these equilibrium states are manifest as steady-state forward or backward crack velocities at specific applied loads. The equilibria are thereby interpreted as quiescent, threshold configurations G = WE, with G the Griffith mechanical-energy-release rate and WE the Dupré work of adhesion, on crack velocity (v-G) diagrams. Generally, WE is found to decrease with concentration of water, in accordance with a Gibbs formalism. Hysteresis is observed in the forward-backward-forward crack propagation cycle, signifying a reduction in the adhesion energy on exposure of the open interface to environmental species prior to healing. This hysteresis is especially marked for those interfaces that are misoriented before healing, indicating that the structure of the underlying solid substrate as well as of the intervening fluid is an important consideration in the interface energetics. The equilibrium states for different environments can be represented on a simple energy-level diagram, as differences between thermodynamic end-point states: initial, closed-interface states refer to crystallographic bonding configurations ahead of the crack-tip adhesion zone; final, open interface states refer to configurations behind the crack-tip zone. The significance of this diagram in relation to the fundamental atomic structure of interfaces in fracture and other adhesion geometries, including implications concerning kinetics, is discussed.