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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".

Deadline for manuscript submissions: 31 March 2026 | Viewed by 10992

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Special Issue Editors

Prof. Dr. Antonio J. Ramirez-Pastor

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Guest Editor

Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Ejército de Los Andes 950, San Luis D5700BWS, Argentina
Interests: statistical thermodynamics; surface phase transitions; lattice-gas models; multisite-occupancy adsorption; Monte Carlo simulations

Prof. Dr. Jose Luis Riccardo

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Guest Editor

Departamento de Física, Instituto de Física Aplicada, Universidad Nacional de San Luis-CONICET, Ejército de Los Andes 950, San Luis D5700BWS, Argentina
Interests: statistical physics; exclusion statistics; adsorption thermodynamics; surface diffusion; Monte Carlo simulations

Special Issue Information

Dear Colleagues,

Lattice gases in classical statistical mechanics is a fascinating and powerful tool for modeling physical systems. Its underlying simplicity presents major theoretical challenges in developing analytical solutions for the thermodynamic functions when particles are structured because their size, form, and composition and differ from ideal. Entropy dependence on density plays a determinant role in the phase behavior of complex lattice gases. The field, far from being only of historical interest, has become of increasing interest due to its fundamental importance, as well as for applications within physical chemistry, biology, material science, and, more recently, quantum computing. Similarly daring become the field of statistical simulations to represent statistical ensembles of particles on strongly correlated states leading to significantly rich phase changes. In regard to quantum lattice gases, its importance as a prototype model of strongly correlated many-body systems for quantum computing as well as the realization of statistics of fractional-like quasi-particles in two dimensions is currently of major fundamental and technological importance. In addition, these theoretical developments in novel quantum statistics find applications in classical systems counterparts helping to understand their thermodynamics from new perspectives. The aim of this Special Issue is to present a number of reviewing and inspiring papers on these issues concerning the analytical treatment and simulation of equilibrium, phase behavior and kinetics of complex classical lattice gases either in classical as well as in quantum model systems.

The topics of interest for this Special Issue include the following:

Fundamentals of Lattice Gases

Equilibrium and non-equilibrium properties
Simulations techniques

Equilibrium Thermodynamics, Phase Transitions, and Critical Phenomena

Phase transitions and universality classes
Critical phenomena and scaling behavior
Applications of lattice gases in modeling phase transitions

Transport Phenomena and Kinetics

Diffusion in lattice gases
Kinetics in lattice gas systems

Complex Lattice Gases

Structured-particle lattice gases
Lattice gases in porous media and heterogeneous systems
Complex networks and interconnected systems

Quantum Lattice Gases

Theoretical frameworks
Phase transitions and quantum phenomena in lattice gas models
Quantum simulation techniques and applications

Contributing authors may select a topic and subtopic of the general proposed index related to their papers. Eventually, authors may suggest alternative or additional subtopics into which their work would fit better.

Prof. Dr. Antonio J. Ramirez-Pastor
Prof. Dr. Jose Luis Riccardo
Guest Editors

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Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

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Keywords

fundamentals of lattice gases
equilibrium thermodynamics
adsorption
phase transitions and critical phenomena
transport phenomena and kinetics
surface diffusion
lattice gases in complex systems
quantum lattice gases

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Published Papers (7 papers)

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Research

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18 pages, 455 KB

Open AccessArticle

Exploring Different Extrapolation Approaches for the Critical Temperature of the 2D-Ising Model Based on Exactly Solvable Finite-Sized Lattices

by Daniel Markthaler and Kai Peter Birke

Entropy 2025, 27(11), 1139; https://doi.org/10.3390/e27111139 - 6 Nov 2025

Viewed by 411

Abstract

The fact that the Ising model in higher dimensions than 1D features a phase transition at the critical temperature

T_{c}

despite its apparent simplicity is one of the main reasons why it has lost none of its fascination and remains a central [...] Read more.

The fact that the Ising model in higher dimensions than 1D features a phase transition at the critical temperature

T_{c}

despite its apparent simplicity is one of the main reasons why it has lost none of its fascination and remains a central benchmark in modeling physical systems. Building on our previous work, where an approximative analytic free-energy expression for finite 2D-Ising lattices was introduced, we investigate different extrapolation strategies for estimating

T_{c}

of the infinite system from exactly solvable small lattices. Finite square lattices of linear dimension N with free and periodic boundary conditions were analyzed, exploiting their exactly accessible density of states to compute the heat capacity profiles

C (T)

. Different approaches were compared, including scaling models for the peak temperature

T_{\max} (N)

and an envelope construction across the set of

C (T)

-profiles. We find that both approaches converge to the same asymptotic value and compare favorably to the established Binder cumulant method. Remarkably, a model for

T_{\max}

with a single model parameter following an

N / (N + 1)

-law provides robust convergence, with a physical analogy motivating this proportionality. Our findings highlight that surprisingly few, but highly accurate, finite-size results are sufficient to obtain a precise extrapolation. Full article

(This article belongs to the Special Issue Statistical Mechanics of Lattice Gases)

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17 pages, 1775 KB

Open AccessArticle

Self-Diffusion in Two-Dimensional Colloidal Systems: A Computer Simulation Study

by Piotr Polanowski and Andrzej Sikorski

Entropy 2025, 27(11), 1091; https://doi.org/10.3390/e27111091 - 22 Oct 2025

Viewed by 547

Abstract

The dynamics of dense colloidal systems are not fully understood. In the study of these types of systems, computer simulations based on the so-called hard sphere model play a significant role. In the presented work, we consider a system of hard spheres of the same size but different mobilities (molecules with high mobility correspond to solvent molecules, while molecules with reduced mobility are colloid particles) at varying concentrations. For this purpose, a two-dimensional lattice and an thermal model of such systems was designed. In order to determine the properties of such systems, a Monte Carlo computer simulation was used, employing the Dynamic Lattice Liquid (DLL) algorithm. Our main aim was to determine how the dynamic behavior of the system in the short time affects the long-time behavior. For this purpose, we investigated the cross-ratios of the diffusion coefficients in the short and long time of the considered system elements. It was found that the reduction in the solvent mobility with increasing concentration of colloidal particles in a short time leads to a very similar reduction in the mobility of the colloid particles in a long time, but we do not observe such behavior in the case of the solvent, i.e., there is a decrease in the value of the solvent diffusion coefficient in the long time with the change in the concentration of colloid particles, but it is difficult to connect it in a simple way with the decrease in the diffusion coefficient in the short time. Full article

(This article belongs to the Special Issue Statistical Mechanics of Lattice Gases)

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20 pages, 3409 KB

Open AccessArticle

Order Lot Sizing: Insights from Lattice Gas-Type Model

by Margarita Miguelina Mieras, Tania Daiana Tobares, Fabricio Orlando Sanchez-Varretti and Antonio José Ramirez-Pastor

Entropy 2025, 27(8), 774; https://doi.org/10.3390/e27080774 - 23 Jul 2025

Viewed by 767

Abstract

In this study, we introduce a novel interdisciplinary framework that applies concepts from statistical physics, specifically lattice-gas models, to the classical order lot-sizing problem in supply chain management. Traditional methods often rely on heuristic or deterministic approaches, which may fail to capture the inherently probabilistic and dynamic nature of decision-making across multiple periods. Drawing on structural parallels between inventory decisions and adsorption phenomena in physical systems, we constructed a mapping that represented order placements as particles on a lattice, governed by an energy function analogous to thermodynamic potentials. This formulation allowed us to employ analytical tools from statistical mechanics to identify optimal ordering strategies via the minimization of a free energy functional. Our approach not only sheds new light on the structural characteristics of optimal planning but also introduces the concept of configurational entropy as a measure of decision variability and robustness. Numerical simulations and analytical approximations demonstrate the efficacy of the lattice gas model in capturing key features of the problem and suggest promising avenues for extending the framework to more complex settings, including multi-item systems and time-varying demand. This work represents a significant step toward bridging physical sciences with supply chain optimization, offering a robust theoretical foundation for both future research and practical applications. Full article

(This article belongs to the Special Issue Statistical Mechanics of Lattice Gases)

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23 pages, 3418 KB

Open AccessArticle

Electrochemical Modeling Applied to Intercalation Phenomena Using Lattice Kinetic Monte Carlo Simulations: Galvanostatic Simulations

by E. Maximiliano Gavilán-Arriazu, Andrés Ruderman, Carlos Bederian, Eduardo Moran Vieyra and Ezequiel P. M. Leiva

Entropy 2025, 27(7), 663; https://doi.org/10.3390/e27070663 - 20 Jun 2025

Viewed by 750

Abstract

In the present work, we address the theory of the lattice-gas model to the study of intercalation materials by using a novel kinetic Monte Carlo (kMC) algorithm for the simulation of an electrochemical method of everyday use in R&D laboratories: constant-current chrono-potentiometric measurements. The main aim of the present approach is to show how to use these atomistic simulations to study intercalation materials used as electrodes in alkali-ion batteries under galvanostatic conditions. The framework can be applied to related areas. To accomplish this, we explain the electrochemical background, linking the continuum scale with the microscopic events of discrete simulations. A comprehensive theoretical approach developed in a previous work is used as a reference for this aim. The galvanostatic kMC algorithm proposed is explained in detail and is subject to validation tests. The present work may serve as a basis for future implementations of kMC under galvanostatic conditions to study phenomena beyond the applicability of simulations on the continuum scale. Full article

(This article belongs to the Special Issue Statistical Mechanics of Lattice Gases)

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20 pages, 3217 KB

Open AccessArticle

Kinetic Monte Carlo Modeling of the Spontaneous Deposition of Platinum on Au(111) Surfaces

by María Cecilia Gimenez, Oscar A. Oviedo and Ezequiel P. M. Leiva

Entropy 2025, 27(6), 619; https://doi.org/10.3390/e27060619 - 11 Jun 2025

Viewed by 1105

Abstract

The spontaneous deposition of platinum (

P t

) atoms on

A u (111)

The spontaneous deposition of platinum (

P t

) atoms on

A u (111)

surfaces is systematically investigated through kinetic Monte Carlo simulations within the Embedded Atom Model framework. The kinetic model aims to capture both stoichiometric, atomic-scale interactions and the more relevant processes that describe the kinetics of a physical problem. Various deposition rates are examined, encompassing a thorough exploration of

P t

adsorption up to a coverage degree of

θ = 0.25

. The resulting 2D islands exhibit a ramified structure, mirroring the experimental methodologies. For the first time, this study extensively analyzes the dependence of both the mean island size and island density on spontaneous deposition, thereby offering valuable insights into the intricate dynamics of the system. Full article

(This article belongs to the Special Issue Statistical Mechanics of Lattice Gases)

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Review

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129 pages, 6810 KB

Open AccessReview

Statistical Mechanics of Linear k-mer Lattice Gases: From Theory to Applications

by Julian Jose Riccardo, Pedro Marcelo Pasinetti, Jose Luis Riccardo and Antonio Jose Ramirez-Pastor

Entropy 2025, 27(7), 750; https://doi.org/10.3390/e27070750 - 14 Jul 2025

Viewed by 1854

Abstract

The statistical mechanics of structured particles with arbitrary size and shape adsorbed onto discrete lattices presents a longstanding theoretical challenge, mainly due to complex spatial correlations and entropic effects that emerge at finite densities. Even for simplified systems such as hard-core linear k-mers, exact solutions remain limited to low-dimensional or highly constrained cases. In this review, we summarize the main theoretical approaches developed by our research group over the past three decades to describe adsorption phenomena involving linear k-mers—also known as multisite occupancy adsorption—on regular lattices. We examine modern approximations such as an extension to two dimensions of the exact thermodynamic functions obtained in one dimension, the Fractional Statistical Theory of Adsorption based on Haldane’s fractional statistics, and the so-called Occupation Balance based on expansion of the reciprocal of the fugacity, and hybrid approaches such as the semi-empirical model obtained by combining exact one-dimensional calculations and the Guggenheim–DiMarzio approach. For interacting systems, statistical thermodynamics is explored within generalized Bragg–Williams and quasi-chemical frameworks. Particular focus is given to the recently proposed Multiple Exclusion statistics, which capture the correlated exclusion effects inherent to non-monomeric particles. Applications to monolayer and multilayer adsorption are analyzed, with relevance to hydrocarbon separation technologies. Finally, computational strategies, including advanced Monte Carlo techniques, are reviewed in the context of high-density regimes. This work provides a unified framework for understanding entropic and cooperative effects in lattice-adsorbed polyatomic systems and highlights promising directions for future theoretical and computational research. Full article

(This article belongs to the Special Issue Statistical Mechanics of Lattice Gases)

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27 pages, 2723 KB

Open AccessReview

Phase Stability and Transitions in High-Entropy Alloys: Insights from Lattice Gas Models, Computational Simulations, and Experimental Validation

by Łukasz Łach

Entropy 2025, 27(5), 464; https://doi.org/10.3390/e27050464 - 25 Apr 2025

Cited by 2 | Viewed by 3434

Abstract

High-entropy alloys (HEAs) are a novel class of metallic materials composed of five or more principal elements in near-equimolar ratios. This unconventional composition leads to high configurational entropy, which promotes the formation of solid solution phases with enhanced mechanical properties, thermal stability, and corrosion resistance. Phase stability plays a critical role in determining their structural integrity and performance. This study provides a focused review of HEA phase transitions, emphasizing the role of lattice gas models in predicting phase behavior. By integrating statistical mechanics with thermodynamic principles, lattice gas models enable accurate modeling of atomic interactions, phase segregation, and order-disorder transformations. The combination of computational simulations (e.g., Monte Carlo, molecular dynamics) with experimental validation (e.g., XRD, TEM, APT) improves predictive accuracy. Furthermore, advances in data-driven methodologies facilitate high-throughput exploration of HEA compositions, accelerating the discovery of alloys with optimized phase stability and superior mechanical performance. Beyond structural applications, HEAs demonstrate potential in functional domains, such as catalysis, hydrogen storage, and energy technologies. This review brings together theoretical modeling—particularly lattice gas approaches—and experimental validation to form a unified understanding of phase behavior in high-entropy alloys. By highlighting the mechanisms behind phase transitions and their implications for material performance, this work aims to support the design and optimization of HEAs for real-world applications in aerospace, energy systems, and structural materials engineering. Full article

(This article belongs to the Special Issue Statistical Mechanics of Lattice Gases)

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