arXiv subjects

J. P. Badiali

Publications and source records attributed to J. P. Badiali.

At least 19 recordsLinked to original sources

arXiv2017

Stochastic simulation of destruction processes in self-irradiated materials

Self-irradiation damages resulting from fission processes are common phenomena observed in nuclear fuel containing (NFC) materials. Numerous $α$-decays lead to local structure transformations in NFC materials. The damages appearing due to the impacts of heavy nuclear recoils in the subsurface layer can cause detachments of material particles. Such a behaviour is similar to sputtering processes observed during a bombardment of the material surface by a flux of energetic particles. However, in the NFC material, the impacts are initiated from the bulk. In this work we propose a two-dimensional mesoscopic model to perform a stochastic simulation of the destruction processes occurring in a subsurface region of NFC material. We describe the erosion of the material surface, the evolution of its roughness and predict the detachment of the material particles. Size distributions of the emitted particles are obtained in this study. The simulation results of the model are in a qualitative agreement with the size histogram of particles produced from the material containing lava-like fuel formed during the Chernobyl nuclear power plant disaster.

cond-mat.mtrl-sci↗

arXiv2015

Role of closed paths in the path integral approach of statistical thermodynamics

Thermodynamics is independent of a description at a microscopic level consequently statistical thermodynamics must produce results independent of the coordinate system used to describe the particles and their interactions. In the path integral formalism the equilibrium properties are cal- culated by using closed paths and an euclidean coordinate system. We show that the calculations on these paths are coordinates independent. In the change of coordinate systems we consider those preserving the physics on which we focus. Recently it has been shown that the path integral formalism can be built from the real motion of particles. We consider the change of coordinates for which the equations of motion are unchanged. Thus we have to deal with the canonical trans- formations. The Lagrangian is not uniquely defined and a change of coordinates introduces in hamiltonians the partial time derivative of an arbitrary function. We have show that the closed paths does not contain any arbitrary ingredients. This proof is inspired by a method used in gauge theory. Closed paths appear as the keystone on which we may describe the equilibrium states in statistical thermodynamics.

cond-mat.stat-mech↗

arXiv2015

Toward a new foundation of statistical thermodynamics

We propose a new approach concerning the introduction of time-irreversibility in statistical mechanics. It is based on a transition function defined in terms of path integral and verifying a time-irreversible equation. We show first how dynamic processes may enter in the description of equilibrium states. In order to do that a characteristic time is associated with closed paths. For large isolated systems at equilibrium or for systems in contact with a thermostat our results are identical with those obtained with the Gibbs ensemble methods. For a model used in the microscopic approaches of the brownian motion no new basic assumption is required to predict a transition from a quantum state to a classical one exhibiting a time-irreversible behavior. This demonstration is sufficient to show that very well accepted approximations can lead to time-irreversible behaviors for a large class of systems. The difference between our work and the system+reservoir approaches is underlined. Here equilibrium states and irreversible processes are described on the same footing representing a progress in the question of time-irreversibility in statistical physics. The transition function is also used for describing a small system for which there is no thermodynamics. By adding to the transition function a second one characterizing the reverse motion we may describe time-reversible systems. In a simple case we replace two real valued transition functions by a complex function verifying a Schrodinger like equation. From this we see how to break the time-reversibility of this equation and how to investigate the connection quantum mechanics-thermodynamics from a very fundamental point of view.

cond-mat.stat-mech↗

arXiv2013

Time evolution of a small reactive system

We investigate the irreversible evolution of a small system in which a chemical reaction takes place. We have two main goals: the first requires to find an equation to produce a time-irreversible behavior,the second consists in introducing a simple exactly solvable model in order to understand basic facts in chemical kinetics. Our basic tool is the transition function counting the number of paths joining two points in the reactive coordinates system. An exact quantum Smoluchowski equation is derived for the reactive system in vacuum, in the presence of a solvent in equilibrium at any time with the reactive system a new Smoluchowski equation is obtained. The transition from a quantum regime to a classical one is discussed. The case of a reactive system not in equilibrium with its neighborhood is investigated in terms of path integral and via a partial differential function. Memory effects and closure assumptions are discussed. Using a simple potential model, the chemical rate constant is exactly calculated and questions such as the meaning of the activation energy or the physical content of the so-called prefactor are investigated.

cond-mat.stat-mech↗

arXiv2013

Modeling of aging processes in the insertion compounds

The aging phenomena occurring in the course of cycling processes in the insertion host-guest compounds are discussed in the framework of a simple model. It takes into account two types of effects. One can be attributed to modifications of the host/guest solution interface in a form of an effective energetic barrier. The other is associated with the host matrix disordering that is translated into a change in the distribution of the host site energies as a function of the applied potential or the concentration of the guest species. It is found that the aging properties depend on the preparation mode, the cycling conditions and the insertion induced transformations. The impact of these transformations on the aging is determined by the matrix sensibility.

cond-mat.mtrl-sci↗

arXiv2013

Phase behavior under the averaging over disorder realizations

Effects of the averaging over disorder realizations (samples) on the phase behavior are analyzed in terms of the mean field approximation for the random field Ising model with infinite range interactions. It is found that the averaging is equivalent to a drastic modification in the statistics of the quenched variables. In its turn, this lowers the critical temperature of a second-order phase transition or, depending on the sampling, even suppresses the ordered phase. Possible first order transitions are shown to be softened by the sample averaging. Common issues and differences in the interpretation of these effects in the context of the simulation and experimental studies are discussed.

cond-mat.stat-mech↗

arXiv2010

A link between the maximum entropy approach and the variational entropy form

The maximum entropy approach operating with quite general entropy measure and constraint is considered. It is demonstrated that for a conditional or parametrized probability distribution $f(x|μ)$ there is a "universal" relation among the entropy rate and the functions appearing in the constraint. It is shown that the recently proposed variational formulation of the entropic functional can be obtained as a consequence of this relation, that is from the maximum entropy principle. This resolves certain puzzling points appeared in the variational approach.

cond-mat.stat-mech↗

arXiv2010

Towards a new approach of quantum dissipation in simple chemical systems

We suggest a new approach for describing quantum dissipation in a small systems for which the system-plus-reservoir approach is not relevant. We first analyze the fact that equilibrium thermodynamics may reveal the existence of an underlying dynamics. This is true in the algebraic approach of quantum mechanics via the Tomita-Takesaki theorem. A similar result is obtained if we start from the path integral expression of the partition function, an equation of motion is introduced. In both cases a parameter has to be identified with the physical time. Several arguments are presented showing that it is so. By investigating the dynamics for short times we introduce an equilibrium condition from which a natural unit of time appears. The equation of motion is extended to non equilibrium situations for which a H-theorem can be derived. The equation of motion can be transformed into a quantum Smoluchovski equation, its solution is a probability having a clear physical meaning. The relaxation of this probability towards its equilibrium value requires a time during which a thermodynamic description is possible or not. A standard bistable model is investigated and the chemical rate $k(t)$ is calculated as a function of time, it appears to be a non monotonic function of time. In some conditions the stationary value of $k(t)$ can be identified with the Kramers result. Finally we compare our approach which is naturally irreversible with an analysis based on the Schrödinger equation which is reversible. From all these results it appears that our equation of motion or its Smoluchovski version appear as a realistic starting point for describing quantum dissipation in small systems.

cond-mat.stat-mech↗

arXiv2009

Relation Time-Thermodynamics. a Path Integral Approach

Starting from an algebraic approach of quantum physics it has been shown via the Tomita-Takesaki theorem and the KMS condition that the canonical density matrix contains the dynamics of the system provided we use a rescaling of time. In this paper we show that the path integral form of the partition function reveals a dynamics which is complementary of the one given by the Tomita-Takesaki theorem. To do that we work in the spirit of a Feynman'conjecture. We define the entropy as a measure of the disorder in space time. By using an equilibrium condition we introduce a natural time scale that it is precisely the one appearing in the Tomita-Takesaki theorem. For this time scale depending on the temperature but not on the system properties our definition of entropy is identical to the thermodynamic one. The underlying dynamics associated with the partition function allows us to derive a $\bf{H}$-$theorem$. It is obtained in the thermodynamic limit and provided we are in a regime in which the thermal fluctuations are larger than the quantum ones.

cond-mat.stat-mech↗

arXiv2008

Simple field theoretical approach of Coulomb systems. Entropic effects

We discuss a new simple field theory approach of Coulomb systems. Using a description in terms of fields, we introduce in a new way the statistical degrees of freedom in relation with the quantum mechanics. We show on a series of examples that these fundamental entropic effects can help account for physical phenomena in relation with Coulomb systems whether symmetric or also asymmetric in valence. On the overall, this gives a new understanding of these systems.

cond-mat.stat-mech↗

arXiv2008

A formally exact field theory for classical systems at equilibrium

We propose a formally exact statistical field theory for describing classical fluids with ingredients similar to those introduced in quantum field theory. We consider the following essential and related problems : i) how to find the correct field functional (Hamiltonian) which determines the partition function, ii) how to introduce in a field theory the equivalent of the indiscernibility of particles, iii) how to test the validity of this approach. We can use a simple Hamiltonian in which a local functional transposes, in terms of fields, the equivalent of the indiscernibility of particles. The diagrammatic expansion and the renormalization of this term is presented. This corresponds to a non standard problem in Feynman expansion and requires a careful investigation. Then a non-local term associated with an interaction pair potential is introduced in the Hamiltonian. It has been shown that there exists a mapping between this approach and the standard statistical mechanics given in terms of Mayer function expansion. We show on three properties (the chemical potential, the so-called contact theorem and the interfacial properties) that in the field theory the correlations are shifted on non usual quantities. Some perspectives of the theory are given.

cond-mat.soft↗

arXiv2007

Incomplete normalization of probability on multifractals

This work is an extension of the incomplete probability theory from the simple case of monofractals previously studied to the more general case of multifractals which can occur in the phase space without equiprobable partition.

cond-mat.stat-mech↗

arXiv2006

Constrained equilibrium as a tool for characterization of deformable porous media

A new method for characterizing the deformable porous materials with non-critical adsorption probes is proposed. The mechanism is based on a driving the adsorbate through a sequence of constrained equilibrium states with the insertion isotherms forming a pseudo-critical point or a van der Waals-type loop. In the framework of a perturbation theory and Monte Carlo simulations we have found a link between the loop parameters and the host morphology. This allows one to characterize porous matrices through analyzing a shift of the pseudo-critical point and a shape of the pseudo-spinodals.

cond-mat.stat-mech↗

arXiv2006

Modelling competitive coadsorption in electrochemical growth processes

We present models of electrodeposition of ZnO films with organic additives, with focus on the growth of hybrid films with eosin Y. First we propose a rate equation model which assumes that the additives form branches with an exposed part above the ZnO deposit, growing with larger rate than the pure film, and that the rate of production of ZnO near those branches is proportional to the height exposed to the solution. This accounts for the production of OH- ions near the branches and the reactions with Zn++ ions. The steady state solution shows both species growing with the rate of the branches, and qualitatively explains their catalytic effect. Subsequently, we propose a more realistic statistical model for the formation of the hybrid deposits from Zn++ ions, a hydroxide precursor and eosin in solution. Simple probabilistic rules are used for reactions of eosin and oxygen, taking into account diffusion from solution along the same lines of the diffusion-limited aggregation models. The catalytic effect is represented by the preferencial production of OH- ions near eosin branches, which form ZnO species. An improvement of the growth rate is possible only with a rather large diffusion coefficient of eosin in solution compared to that of hydroxide precursors, in agreement with experimental findings. In the cases where a series of neighboring eosin clusters competitively grow, the increase in the growth rate and the high eosin loading observed in the simulated deposits also agree qualitatively with electrodeposition experiments.

physics.chem-ph↗

arXiv2006

On a mechanism low-pressure insertion of chain molecules into crystalline matrices

A microscopic mechanism of low-pressure insertion and separation of chain-like molecules in host matrices is proposed. It is shown that the intramolecular correlations combined to appropriate host activities are responsible for a low-pressure condensation of chain molecules. This allows recover a fine structure of the isotherms and to explain recent experiments on the insertion of $C_2H_2$ and $CO_2$ guest species. We argue that the mechanism should be dominant in low-dimensional host geometries, where the entropic effects are strongly suppressed and the major factors are the chain connectivity and packing.

cond-mat.stat-mech↗

arXiv2006

Maximum entropy approach to power-law distributions in coupled dynamic-stochastic systems

Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a power-law statistics are investigated. It is demonstrated that, from a quite general point of view, the power-law dependencies may appear as a consequence of "global" constraints restricting both the dynamic phase space and the stochastic fluctuations. As a result, at sufficiently long observation times the dynamic counterpart is driven into a non-equilibrium steady state whose deviation from the usual exponential statistics is given by the distance from the conventional equilibrium.

cond-mat.stat-mech↗

arXiv2006

Negative linear compressibility in confined dilatating systems

The role of a matrix response to a fluid insertion is analyzed in terms of a perturbation theory and Monte Carlo simulations applied to a hard sphere fluid in a slit of fluctuating density-dependent width. It is demonstrated that a coupling of the fluid-slit repulsion, spatial confinement and the matrix dilatation acts as an effective fluid-fluid attraction, inducing a pseudo-critical state with divergent linear compressibility and non-critical density fluctuations. An appropriate combination of the dilatation rate, fluid density and the slit size leads to the fluid states with negative linear compressibility. It is shown that the switching from positive to negative compressibility is accompanied by an abrupt change in the packing mechanism.

cond-mat.stat-mech↗

arXiv2005

Entropy: From Black Holes to Ordinary Systems

Several results of black holes thermodynamics can be considered as firmly founded and formulated in a very general manner. From this starting point we analyse in which way these results may give us the opportunity to gain a better understanding in the thermodynamics of ordinary systems for which a pre-relativistic description is sufficient. First, we investigated the possibility to introduce an alternative definition of the entropy basically related to a local definition of the order in a spacetime model rather than a counting of microstates. We show that such an alternative approach exists and leads to the traditional results provided an equilibrium condition is assumed. This condition introduces a relation between a time interval and the reverse of the temperature. We show that such a relation extensively used in the black hole theory, mainly as a mathematical trick, has a very general and physical meaning here; in particular its derivation is not related to the existence of a canonical density matrix. Our dynamical approach of thermodynamic equilibrium allows us to establish a relation between action and entropy and we show that an identical relation exists in the case of black holes. The derivation of such a relation seems impossible in the Gibbs ensemble approach of statistical thermodynamics. From these results we suggest that the definition of entropy in terms of order in spacetime should be more general that the Boltzmann one based on a counting of microstates. Finally we point out that these results are obtained by reversing the traditional route going from the Schrödinger equation to statistical thermodynamics.

gr-qc↗