The Mathematics of Statistical Mechanics and Its Applications

Dear Colleagues,

Statistical mechanics is a powerful framework connecting microscopic laws, probabilistic structures, and emergent macroscopic behavior with applications in mathematics and physics, but also across many other disciplines, such as economics, social sciences, biology, etc. This Special Issue welcomes contributions that either involve the mathematical foundations of statistical mechanics and advance the analytical methods on which it relies, or focus on computational approaches, modeling, and simulation in complex systems across disciplines. We invite original research and high-quality reviews that clarify rigorous theory, develop new methods, or demonstrate the relevance of statistical-mechanical ideas in contemporary scientific and technological problems.

Suggested topics include, but are not limited to, the following:

• Rigorous foundations of equilibrium and non-equilibrium statistical mechanics;
• Non-extensive, generalized, fractional, and anomalous statistical-mechanical frameworks (e.g., Tsallis statistics);
• New mathematical models and computational tools for interdisciplinary applications;
• Gibbs measures, thermodynamic limits, ensemble equivalence, and phase-space methods;
• Phase transitions and critical phenomena;
• Universality and renormalization-group methods;
• Large deviations, fluctuation theorems, entropy production, and rare-event theory;
• Ergodic theory, mixing, dynamical systems, chaos, and microscopic reversibility;
• Kinetic theory, Boltzmann-type equations, hydrodynamic limits, and transport phenomena;
• Stochastic processes, Markov dynamics, interacting particle systems, and random walks;
• Exactly solvable models, spin systems, lattice gases, percolation, and random media;
• Quantum statistical mechanics, open quantum systems, quantum information, and many-body theory;
• Random matrix theory, spectral methods, graph theory, and complex-network approaches;
• Information theory, inference, Bayesian methods, maximum entropy, and statistical learning;
• Numerical and computational statistical mechanics, including Monte Carlo and molecular dynamics, hybrid methods (e.g., Nose-Hoover thermostat);
• Multiscale modeling, coarse graining, reduced-order models, and uncertainty quantification;
• Machine learning, data-driven discovery, reservoir computing, and AI-assisted modeling;
• Materials science, condensed matter, nanostructures, defects, and electronic transport;
• Biophysics, systems biology, neuroscience, protein dynamics, and evolutionary processes;
• Chemical physics, reaction networks, self-organization, and pattern formation;
• Plasma physics, astrophysics, geophysics, climate dynamics, and turbulent systems;
• Epidemic modeling, population dynamics, ecology, and collective behavior;
• Econophysics, financial markets, social systems, urban dynamics, and decision processes;
• Energy systems, smart grids, optimization, reliability, and statistical-mechanical control.

Submissions may be theoretical, computational, methodological, or application-driven, provided that they make a clear connection to principles or methods of statistical mechanics.

Prof. Dr. Ioannis P. Antoniades
Prof. Dr. Lazaros Gallos
Prof. Dr. Panos Argyrakis
Guest Editors

Manuscript Submission Information

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. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• statistical mechanics: mathematical methods
• complex networks
• phase transitions and critical phenomena
• interdisciplinary methods and applications of statistical mechanics