Advanced Statistical Mechanics

In fact, statistical physics is so general that it still holds, in a much wider context, than that, on which the original theory was developed. Consequently, despite its largely recognized success in physics, considerable efforts have been made to extend the formalism of statistical physics, beyond its original application. In this way, an increasing amount of physical and physical-like systems are now well-studied by using the standard tools of this theory. Entropy is a very important quantity and plays a key role in many aspects of statistical mechanics and information theory. Thus, in the last decades, an intense research activity that has modified our comprehension of statistical physics, extending and renewing its applicability, considerably.

This book presents the state of the art advances and trends made in Statistical Mechanics of the past several years. Although long assumed to have an important role in the suppression of crystallization and the development of glass formers, the effect of local fivefold symmetry has never been directly tested. The book opens with a study that considers whether such suppression of crystallization has a kinetic or thermodynamic nature and investigates its mechanism.

This book next proposes a generalization of a complexity measure and applies it to a two-level system and a system obeying exponential distribution. Further, the book focuses on spectral functions and properties of nuclear matter; statistical mechanics for weak measurements and quantum inseparability; statistical description of nonrelativistic classical systems; Bayesian statistical mechanics: entropy-enthalpy compensation and universal equation of state at the tip of pen energy from negentropy of non-chaotic systems; and randomization of energy and momentum in statistical mechanics.

An alternative approach to particle-particle collisions is explored further. The book closes with a chapter that presents rigorous proof of the aforementioned exact mapping equivalence is provided by two independent approaches exploiting either a graph-theoretical or spin representation of the zero-field eight-vertex model. Influence of the interaction anisotropy, as well as the uniaxial single-ion anisotropy on phase transitions and critical phenomena, are examined in particular. It will be demonstrated that the critical exponents of the mixed spin-1/2 and spin-S Ising model with the triplet interaction on the central square lattice fundamentally depend on the interaction anisotropy, the uniaxial single-ion anisotropy, as well as, the spin parity. This exclusive book on advanced statistical mechanics offers an advanced approach with frequent applications to the modern problems students and practitioners are confronted with.