arXiv subjects

Tânia Tomé

Publications and source records attributed to Tânia Tomé.

At least 19 recordsLinked to original sources

arXiv2026

Derivation of Fokker-Planck equation and its entropy production

We derive the Fokker-Planck equation and its entropy production from the master equation. To this end we consider a discrete space of states where the master equation is defined and appropriate transition rates are introduced. A transition rate has two parts, one of which is the ordinary term proportional to the inverse of the spacing and the other is inversely proportional to the square of the spacing corresponding to the variance of the independent stochastic variable. In the continuous space limit, we obtain the Fokker-Planck as well as the rate of entropy production and the flux of entropy. We also consider the case where the space of states is the phase space and discuss the equations appropriate for systems in contact with several heat reservoirs and for isolated systems.

cond-mat.stat-mech↗

arXiv2025

Irreversible thermodynamics and Glansdorff-Prigogine principle derived from stochastic thermodynamics

We derive the main equations of irreversible thermodynamic including the expression for the Glansdorff-Prigogine extremal principle from stochastic thermodynamics. To this end, we analyze a system that is subject to gradients of temperature and external forces that induce the appearance of fluxes of several sorts and the creation of entropy. We show that the rate of entropy production is a convex function of the fluxes, from which follows that the excess entropy production is nonnegative, which is an expression of the Glansdorff-Prigogine principle. We show that the Lyapunov function associated with the excess entropy production can be identified with a thermodynamic potential in the special case where the gradients of temperature are absent.

cond-mat.stat-mech↗

arXiv2023

Numerical exploration of the Aging effects in spin systems

An interesting concept that has been underexplored in the context of time-dependent simulations is the correlation of total magnetization, $C(t)$%. One of its main advantages over directly studying magnetization is that we do not need to meticulously prepare initial magnetizations. This is because the evolutions are computed from initial states with spins that are independent and completely random. In this paper, we take an important step in demonstrating that even for time evolutions from other initial conditions, $C(t_{0},t)$, a suitable scaling can be performed to obtain universal power laws. We specifically consider the significant role played by the second moment of magnetization. Additionally, we complement the study by conducting a recent investigation of random matrices, which are applied to determine the critical properties of the system. Our results show that the aging in the time series of magnetization influences the spectral properties of matrices and their ability to determine the critical temperature of systems.

cond-mat.stat-mech↗

arXiv2022

Stochastic thermodynamics of opinion dynamics

We show that models of opinion formation and dissemination in a community of individuals can be framed within stochastic thermodynamics from which we can build a nonequilibrium thermodynamics of opinion dynamics. This is accomplished by decomposing the original transition rate that defines an opinion model into two or more transition rates, each representing the contact with heat reservoirs at different temperatures, and postulating an energy function. As the temperatures are distinct, heat fluxes are present even at the stationary state and linked to the production of entropy, the fundamental quantity that characterizes nonequilibrium states. We apply the present framework to a generic-vote model including the majority-vote model in a square lattice and in a cubic lattice. The fluxes and the rate of entropy production are calculated by numerical simulation and by the use of a pair approximation.

cond-mat.stat-mech↗

arXiv2022

Stochastic motion in phase space on a surface of constant energy

We study closed systems of particles that are subject to stochastic forces in addition to the conservative forces. The stochastic equations of motion are set up in such a way that the energy is strictly conserved at all times. To ensure this conservation law, the evolution equation for the probability density is derived using an appropriate interpretation of the stochastic equation of motion that is not the Itô nor the Stratonovic interpretation. The trajectories in phase space are restricted to the surface of constant energy. Despite this restriction, the entropy is shown to increase with time, expressing irreversible behavior and relaxation to equilibrium. This main result of the present approach contrasts with that given by the Liouville equation, which also describes closed systems, but does not show irreversibility.

cond-mat.stat-mech↗

arXiv2021

Effect of immunization through vaccination on the SIS epidemic spreading model

We analyze the susceptible-infected-susceptible model for epidemic spreading in which a fraction of the individuals become immune by vaccination. This process is understood as a dilution by vaccination, which decreases the fraction of the susceptible individuals. For a nonzero fraction of vaccinated individuals, the model predicts a new state in which the disease spreads but eventually becomes extinct. The new state emerges when the fraction of vaccinated individuals is greater than a critical value. The model predicts that this critical value increases as one increases the infection rate reaching an asymptotic value, which is strictly less than the unity. Above this asymptotic value, the extinction occurs no matter how large the infection rate is.

q-bio.PE↗

arXiv2020

Epidemic spreading

We present an analysis of six deterministic models for epidemic spreading. The evolution of the number of individuals of each class is given by ordinary differential equations of the first order in time, which are set up by using the laws of mass action providing the rates of the several processes that define each model. The epidemic spreading is characterized by the frequency of new cases, which is the number of individuals that are becoming infected per unit time. It is also characterized by the basic reproduction number, which we show to be related to the largest eigenvalue of the stability matrix associated with the disease-free solution of the evolution equations. We also emphasize the analogy between the outbreak of an epidemic with a critical phase transition. When the density of the population reaches a critical value the spreading sets in, a result that was advanced by Kermack and McKendrick in their study of a model in which the recovered individuals acquire permanent immunization, which is one of the models analyzed here.

physics.bio-ph↗

arXiv2020

Stochastic approach to epidemic spreading

We analyze four models of epidemic spreading using a stochastic approach in which the primary stochastic variables are the numbers of individuals in each class. The stochastic approach is described by a master equation and the transition rate for each process such as infection or recovery are set up by using the law of mass action. We perform numerical simulations as well as numerical integration of the evolution equations for the average number of each class of individuals. The onset of the epidemic spreading is obtained by a linear analysis of the disease free state, from which follows the initial exponential increase of the infected and the frequency of new cases. The order parameter and the variance in the number of individuals are also obtained characterizing the onset of epidemic spreading as a critical phase transition.

cond-mat.stat-mech↗

arXiv2020

Analysis of the earlier times and flux of the entropy on the majority voter model with difusion

We study the properties of nonequilibrium systems modelled as spin models without defined Hamiltonian as the majority voter model. This model has transition probabilities that do not satisfy the condition of detailed balance. The lack of detailed balance leads to entropy production phenomena, which are a hallmark of the irreversibility. By considering that voters can diffuse on the lattice we analyze how the entropy production and how the critical properties are affected by this diffusion. We also explore two important aspects of the diffusion effects on the majority voter model by studying entropy production and entropy flux via time-dependent and steady state simulations. This study is completed by calculating some critical exponents as function of the diffusion probability.

cond-mat.stat-mech↗

arXiv2018

Stochastic thermodynamics and entropy production of chemical reaction systems

We investigate the nonequilibrium stationary states of systems consisting of chemical reactions among molecules of several chemical species. To this end we introduce and develop a stochastic formulation of nonequilibrium thermodynamics of chemical reaction systems based on a master equation defined on the space of microscopic chemical states, and on appropriate definitions of entropy and entropy production, The system is in contact with a heat reservoir, and is placed out of equilibrium by the contact with particle reservoirs. In our approach, the fluxes of various types, such as the heat and particle fluxes, play a fundamental role in characterizing the nonequilibrium chemical state. We show that the rate of entropy production in the stationary nonequilibrium state is a bilinear form in the affinities and the fluxes of reaction, which are expressed in terms of rate constants and transition rates, respectively. We also show how the description in terms of microscopic states can be reduced to a description in terms of the numbers of particles of each species, from which follows the chemical master equation. As an example, we calculate the rate of entropy production of the first and second Schlögl reaction models.

cond-mat.stat-mech↗

arXiv2015

Entropy production in linear Langevin systems

We study the entropy production rate in systems described by linear Langevin equations, containing mixed even and odd variables under time reversal. Exact formulas are derived for several important quantities in terms only of the means and covariances of the random variables in question. These include the total rate of change of the entropy, the entropy production rate, the entropy flux rate and the three components of the entropy production. All equations are cast in a way suitable for large-scale analysis of linear Langevin systems. Our results are also applied to different types of electrical circuits, which suitably illustrate the most relevant aspects of the problem.

cond-mat.stat-mech↗

arXiv2015

Stochastic approach to equilibrium and nonequilibrium thermodynamics

We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of entropy itself and the second, the definition of entropy production rate which is nonnegative and vanishes in thermodynamic equilibrium. Based on these assumptions we study interacting systems with many degrees of freedom in equilibrium or out of thermodynamic equilibrium, and how the macroscopic laws are derived from the stochastic dynamics. These studies include the quasi-equilibrium processes, the convexity of the equilibrium surface, the monotonic time behavior of thermodynamic potentials, including entropy, the bilinear form of the entropy production rate, the Onsager coefficients and reciprocal relations, and the nonequilibrium steady states of chemical reactions.

cond-mat.stat-mech↗

arXiv2015

Critical properties of the susceptible-exposed-infected model on a square lattice

The critical properties of the stochastic susceptible-exposed-infected model on a square lattice is studied by numerical simulations and by the use of scaling relations. In the presence of an infected individual, a susceptible becomes either infected or exposed. Once infected or exposed, the individual remains forever in this state. The stationary properties are shown to be the same as those of isotropic percolation so that the critical behavior puts the model into the universality class of dynamic percolation.

cond-mat.stat-mech↗

arXiv2015

Critical behavior in lattice models with two symmetric absorbing state

We analyze nonequilibrium lattice models with up-down symmetry and two absorbing states by mean-field approximations and numerical simulations in two and three dimensions. The phase diagram displays three phases: paramagnetic, ferromagnetic and absorbing. The transition line between the first two phases belongs to the Ising universality class and between the last two, to the direct percolation universality class. The two lines meet at the point describing the voter model and the size $\ell$ of the ferromagnetic phase vanishes with the distance $\varepsilon$ to the voter point as $\ell\sim\varepsilon$, with possible logarithm corrections in two dimensions.

cond-mat.stat-mech↗

arXiv2012

Stochastic dynamics of dengue epidemics

We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, like dengue, and the threshold of the disease. The coexistence space is composed by two structures representing the human and mosquito populations. The human population follows a susceptible-infected-recovered (SIR) type dynamics and the mosquito population follows a susceptible-infected-susceptible (SIS) type dynamics. The human infection is caused by infected mosquitoes and vice-versa so that the SIS and SIR dynamics are interconnected. We develop a truncation scheme to solve the evolution equations from which we get the threshold of the disease and the reproductive ratio. The threshold of the disease is also obtained by performing numerical simulations. We found that for certain values of the infection rates the spreading of the disease is impossible whatever is the death rate of infected mosquito.

q-bio.PE↗

arXiv2012

Exact correlation functions in particle-reaction models with immobile particles

Exact results on particle-densities as well as correlators in two models of immobile particles, containing either a single species or else two distinct species, are derived. The models evolve following a descent dynamics through pair-annihilation where each particle interacts at most once throughout its entire history. The resulting large number of stationary states leads to a non-vanishing configurational entropy. Our results are established for arbitrary initial conditions and are derived via a generating-function method. The single-species model is the dual of the 1D zero-temperature kinetic Ising model with Kimball-Deker-Haake dynamics. In this way, both infinite and semi-infinite chains and also the Bethe lattice can be analysed. The relationship with the random sequential adsorption of dimers and weakly tapped granular materials is discussed.

cond-mat.stat-mech↗

arXiv2010

Finite-size scaling of the stochastic susceptible-infected-recovered model

The critical behavior of the stochastic susceptible-infected-recovered model on a square lattice is obtained by numerical simulations and finite-size scaling. The order parameter as well as the distribution in the number of recovered individuals is determined as a function of the infection rate for several values of the system size. The analysis around criticality is obtained by exploring the close relationship between the present model and standard percolation theory. The quantity UP, equal to the ratio U between the second moment and the squared first moment of the size distribution multiplied by the order parameter P, is shown to have, for a square system, a universal value 1.0167(1) that is the same as for site and bond percolation, confirming further that the SIR model is also in the percolation class.

cond-mat.dis-nn↗

arXiv2010

Aging and stationary properties of non-equilibrium symmetrical three-state models

We consider a non-equilibrium three-state model whose dynamics is Markovian and displays the same symmetry as the three-state Potts model, i.e., the transition rates are invariant under the permutation of the states. Unlike the Potts model, detailed balance is in general not satisfied. The aging and the stationary properties of the model defined on a square lattice are obtained by means of large-scale Monte Carlo simulations. We show that the phase diagram presents a critical line, belonging to the three-state Potts universality class, that ends at a point whose universality class is that of the voter model. Aging is considered on the critical line, at the voter point and in the ferromagnetic phase.

cond-mat.stat-mech↗