Statistical Physics

Statistical physics is a branch of modern physics that employs probability theory and statistical tools to inquire about the physical properties of systems formed by many degrees of freedom.

Although its origin can be traced back to the last decades of the 1800s, when a young Ludwig Boltzmann, with his kinetic theory of gas, was the first to introduce the existence of monads in a modern key and then to highlight the necessity of employing statistical methods in physics. Statistical physics has undergone rapid development during the 1900s thanks to its successes in solving physical problems with large populations and clarifying various observed phenomena such as phase transition, conduction of heat and electricity, and others which until then lacked a clear explanation within the existent theories.

Today, statistical physics is articulated into two main sections:

• Classical statistical mechanics: basically, developed to give a rational understanding of thermodynamics in terms of microscopic particles and their interactions.
• Quantum statistical mechanics: developed to incorporate quantum peculiarities like indistinguishability and entanglements into the theory as sources of novel statistical effects.

However, in recent decades we have seen a phase of rapid change where the field of applicability of statistical physics is constantly increasing. Although traditional statistical physics focuses on systems with many degrees of freedom, it is now well recognized that it can be successfully applied to an increasing number of physical and physical-like systems that seem to not comply with the thermodynamic limit. In this way, new ideas and concepts permitted a fresh approach to old problems. With new concepts, we mean to look for features that were ignored in previous experiments that lead to new exciting results. For instance, a constantly increasing number of situations are known to violate the predictions of orthodox statistical mechanics. Systems where these emerging features are observed seem to not fulfil the standard ergodic and mixing properties on which the Boltzmann–Gibbs formalism is founded. These systems are characterized by a phase space that self-organizes in a (multi)fractal structure, and are governed by nonlinear dynamics, which establishes a deep relation among the parts where the system is formed. Consequently, the problem regarding the relationship between statistical and dynamical laws becomes highlighted, leading to new fields of research that characterizes the disordered systems, such as deterministic chaos, self-organized criticality, turbulence, and intermittency, to cite a few.

The statistical physics section, broad and interdisciplinary in scope, intends to focus on the challenges of modern statistical physics and its applications to borderline problems while incorporating a high degree of mathematical rigor. Its aim is to provide a collection of high-quality research papers that meet the interest not only of physicists working in this field but also mathematicians and engineers interested in interdisciplinary topics. Generally, papers in pure statistics will not be accepted. Download Section Flyer  

Dr. Antonio M. Scarfone
Section Editor-in-Chief

Theoretical Aspects 

• Classical, quantum, and relativistic statistical physics; 
• Kinetic theory (Boltzmann, Fokker-Planck, Smoluchowski and mean-field equations); 
• Statistical physics of many-particle systems, classical and quantum fields; 
• Mathematical statistics and combinatorial aspects of statistical physics; 
• Geometric applications to statistical physics and geometrothermodynamics; 
• Information geometry and Fisher information; 
• Quantum information and entangled states; 
• Non-extensive statistical mechanics and weak ergodicity breaking; 
• Metastability and noise-induced phenomena in complex systems 
• Transport and diffusion processes in dynamical systems; 
• Anomalous diffusion; 
• Chaos and complexity in dynamical systems; 
• Hamiltonian chaos and geodesic flows; 
• Long-range interactions and correlated system; 
• Dynamical processes and relaxation phenomena; 
• Non-equilibrium statistical mechanics and irreversibility; 
• Phase transitions and critical phenomena; 
• Classical and quantum stochastic processes; 
• Open quantum systems and quantum phase transitions; 
• Random, fractional and (multi)-fractals dynamics; 
• Stochastic multiscale modeling; 
• Anomalous distributions, power-laws and Levy distributions; 
• Extreme statistics. 

Applications to Physical Systems 

• Monte Carlo simulations; 
• Statistical physics of complex and disordered systems; 
• Complexity and criticality in condensed matter; 
• Plasma physics; 
• Fluid dynamics; 
• Turbulence; 
• Magnetohydrodynamics; 
• Porous media and granular materials; 
• Pattern formation; 
• Disordered and glassy systems; 
• Surface effects and films; 
• Growth processes; 
• Wetting; 
• Percolation; 
• Spin glasses; 
• Aging; 
• Random walks; 
• Cellular automata; 
• Crystal nucleation and roughening; 
• Liquid crystals and confined liquids; 
• Low dissipation systems. 

Applications to non-Physical Systems 

• Theoretical and mathematical physics in molecular dynamics simulation; 
• Genomics, ecological and evolutionary systems; 
• Soft and biological matter; 
• Brain neuronal networks and biological network models; 
• Climate and earth models (including seismology); 
• Traffic flow; 
• Nonlinear time series analysis; 
• Big data analysis and algorithm problems; 
• Rare events; 
• Statistical physics of disordered systems; 
• Modeling of complex systems; 
• Statistical mechanics on complex networks and graphs; 
• Collective phenomena in economic and social systems; 
• Nanoscale devices; 
• Multi-agent systems; 
• Emergence and evolution of language; 
• Population dynamics; 
• Applications of statistical mechanics to computer sciences 
• Information theory and learning machine; 
• Reinforcement learning; 
• Adaptive control and control of chaos; 
• Opinion formation.