arXiv subjects

Joaquín Peralta

Publications and source records attributed to Joaquín Peralta.

10 recordsLinked to original sources

arXiv2026

Kinetic energy fluctuations and specific heat in generalized ensembles

We derive an exact generalization of the well-known Lebowitz--Percus--Verlet (LPV) formula that relates the kinetic energy fluctuations of an isolated system to its specific heat. Our general formula, obtained by the application of expectation identities, is valid for arbitrary steady--state ensembles and system sizes, expressing the relative variance of the kinetic energy in terms of the variance of total energy and the microcanonical specific heat. The usual microcanonical LPV formula can be readily recovered as a particular case where energy fluctuations vanish. We test the validity of the generalized formula by performing Monte Carlo simulations of a superstatistical system of harmonic oscillators, as well as by exact calculation of energy variances in a uniform--energy ensemble, discussing its relevance to systems exhibiting negative heat capacity and ensemble inequivalence, as encountered in finite nuclei and self--gravitating models. Our results may provide useful in the study of non-equilibrium phase transitions in finite systems.

cond-mat.stat-mech↗

arXiv2024

Superstatistics as the thermodynamic limit of driven classical systems

Superstatistics is an elegant framework for the description of steady-state thermodynamics, mostly used for systems with long-range interactions such as plasmas. In this work, we show that the potential energy distribution of a classical system under externally imposed energy fluctuations can also be described by superstatistics in the thermodynamic limit. As an example, we apply this formalism to the thermodynamics of a finite Lennard-Jones crystal with constant microcanonical heat capacity driven by sinusoidal energy oscillations. Our results show that molecular dynamics simulations of the Lennard-Jones crystal are in agreement with the provided theoretical predictions.

cond-mat.stat-mech↗

arXiv2022

Configurational density of states and melting of simple solids

We analyze the behavior of the microcanonical and canonical caloric curves for a piecewise model of the configurational density of states of simple solids, in the context of melting from the superheated state, as realized numerically in the Z-method via atomistic molecular dynamics. A first-order phase transition with metastable regions is reproduced by the model, being therefore useful to describe aspects of the melting transition. Within this model, transcendental equations connecting the superheating limit, the melting point, and the specific heat of each phase are presented and numerically solved. Our results suggest that the essential elements of the microcanonical Z curves can be extracted from simple modeling of the configurational density of states.

cond-mat.stat-mech↗

arXiv2021

A portable and flexible implementation of the Wang--Landau algorithm in order to determine the Density of States

In this work we develop an implementation of the Wang--Landau algorithm [Phys. Rev. Lett. \textbf{86}, 2050-2053 (2001)]. This algorithm allows us to find the density of states (DOS), a function that, for a given system, describes the proportion of states that have a certain energy. The implementation uses the Python language for the algorithm itself, and it can take advantage of any library, such as the powerful LAMMPS library, for the computation of energy. Therefore, the resulting implementation is simple and flexible without sacrificing efficiency. This implementation also considers recent developments in the parallelization of the code for faster computation. We establish the soundness and effectiveness of our implementation by studying well-known systems such as the Ising model, the Lennard--Jones and EAM solids. We have found that our implementation can find the DOS with very good precision in a reasonable amount of time. Therefore, we are equipped with a very powerful and flexible implementation that can be easily used in order to study more realistic models of matter.

cond-mat.stat-mech↗

arXiv2021

A novel Bayesian approach to the computation of the configurational density of states

In this work we develop and implement a novel Bayesian method for computing the DOS of a system. This method is based on the use of a test function with adjustable parameters and we use Bayes theorem to find the best parameters given a certain number of measurements done on the system. This measurements can be done in any ensemble defined by a distribution function. We found that the algorithm can find the DOS in a reasonable amount of time, and that if the test function is suitable enough, the DOS found by the algorithm is very close to the true DOS.

cond-mat.stat-mech↗

arXiv2020

Superheated solid state induced by a single collision event

High-energy incident particles from both pulsed and continuous radiation sources can induce significant damage to the structure of a material by creating vacancy-interstitial pairs and other more complex defects, and this leads typically to localized melting. In this work, we present evidence via molecular dynamics simulations of a superheated solid state in BCC tungsten induced by single PKA events of $\sim$ 1.5 keV of energy. Despite the striking difference between this highly inhomogeneous energy injection and homogeneous melting, the lifetime of the obtained superheated solid state, reaching up to 200 ps, is described through a waiting time distribution in agreement with previous studies on superheating in the Z-method methodology.

cond-mat.mtrl-sci↗

arXiv2017

Deterministic physical systems under uncertain initial conditions: the case of maximum entropy applied to projectile motion

The kinematics and dynamics of deterministic physical systems have been a foundation of our understanding of the world since Galileo and Newton. For real systems, however, uncertainty is largely present via external forces such as friction or lack of precise knowledge about the initial conditions of the system. In this work we focus in the latter case and describe the use of inference methodologies in solving the statistical properties of classical systems subject to uncertain initial conditions. In particular we describe the application of the formalism of Maximum Entropy (MaxEnt) inference to the problem of projectile motion given information about the average horizontal range over many realizations. By using MaxEnt we can invert the problem and use the provided information on the average range to reduce the original uncertainty in the initial conditions, while also achieving additional insights based on the shape of the posterior probabilities for the initial conditions probabilities and the projectile path distribution itself. The wide applicability of this procedure, as well as its ease of use, reveals a useful tool by which to revisit a large number of physics problems, from classrooms to frontier research.

cond-mat.stat-mech↗

arXiv2017

Bayesian statistical modelling of microcanonical melting times at the superheated regime

Homogeneous melting of superheated crystals at constant energy is a dynamical process, believed to be triggered by the accumulation of thermal vacancies and their self-diffusion. From microcanonical simulations we know that if an ideal crystal is prepared at a given kinetic energy, it takes a random time $t_w$ until the melting mechanism is actually triggered. In this work we have studied in detail the statistics of $t_w$ for melting at different energies by performing a large number of Z-method simulations and applying state-of-the-art methods of Bayesian statistical inference. By focusing on the short-time tail of the distribution function, we show that $t_w$ is actually gamma-distributed rather than exponential (as asserted in previous work), with decreasing probability near $t_w \sim 0$. We also explicitly incorporate in our model the unavoidable truncation of the distribution function due to the limited total time span of a Z method simulation. The probabilistic model presented in this work can provide some insight into the dynamical nature of the homogeneous melting process, as well as giving a well-defined practical procedure to incorporate melting times from simulation into the Z-method in order to reduce the uncertainty in the melting temperature.

cond-mat.stat-mech↗

arXiv2014

Statistical distribution of thermal vacancies close to the melting point

A detailed description of the statistical distribution of thermal vacancies near the melting point is presented, using copper as an example. As the temperature is increased, the average number of thermal vacancies generated by atoms migrating to neighboring sites also increase, according to Arrhenius' law. We present for the first time a model for the distribution of thermal vacancies, which according to our results follow a Gamma distribution. All the simulations are carried out by classical molecular dynamics and the recognition of vacancies is achieved via a recently developed algorithm. Our results could be useful in the further development of a theory explaining the mechanism of homogeneous melting, which seems to be mediated (at least in part) by the accumulation of thermal vacancies near the melting point.

cond-mat.mtrl-sci↗

arXiv2014

A Bayesian interpretation of abrupt phase transitions

The formalism used in describing the thermodynamics of abrupt (or first-order) phase transitions is reviewed as an application of maximum entropy inference. In this treatment, we show that the concepts of transition temperature, latent heat and entropy difference between phases will inevitably have an equivalent in any problem of inferring the result of a yes/no question, given information in the form of expectation values.

cond-mat.stat-mech↗