This book deals with an important class of many-body systems: those where the interaction potential decays slowly for large inter-particle distances; in particular, systems where the decay is slower than the inverse inter-particle distance raised to the dimension of the embedding space. Gravitational and Coulomb interactions are the most prominent examples, however it has become clear that long-range interactions are more common than previously thought. A satisfactory understanding of properties, generally considered as oddities only a couple of decades ago, has now been reached: ensemble inequivalence, negative specific heat, negative susceptibility, ergodicity breaking, out-of-equilibrium quasi-stationary-states, anomalous diffusion. The book, intended for Master and PhD students, tries to gradually acquaint the reader with the subject. The first two parts describe the theoretical and computational instruments needed to address the study of both equilibrium and dynamical properties of systems subject to long-range forces. The third part of the book is devoted to applications of such techniques to the most relevant examples of long-range systems.

In memory of Dr. George Zaslavsky, "Long-range Interactions, Stochasticity and Fractional Dynamics" covers the recent developments of long-range interaction, fractional dynamics, brain dynamics and stochastic theory of turbulence, each chapter was written by established scientists in the field. The book is dedicated to Dr. George Zaslavsky, who was one of three founders of the theory of Hamiltonian chaos. The book discusses self-similarity and stochasticity and fractionality for discrete and continuous dynamical systems, as well as long-range interactions and diluted networks. A comprehensive theory for brain dynamics is also presented. In addition, the complexity and stochasticity for soliton chains and turbulence are addressed. The book is intended for researchers in the field of nonlinear dynamics in mathematics, physics and engineering. Dr. Albert C.J. Luo is a Professor at Southern Illinois University Edwardsville, USA. Dr. Valentin Afraimovich is a Professor at San Luis Potosi University, Mexico.

This book collects lectures and seminars given at the Les Houches Summer School 2008 on Long-Range Interacting Systems. It reviews state-of-the-art developments in this field, looking at problems of probability, transport theory, statistical mechanics, condensed matter physics, astrophysics and cosmology, physics of plasmas, and hydrodynamics.

The workshop was about the developments of the thermodynamical and dynamical behavior of many-body systems in which the interactions decay very slowly with the distance: they present very strange properties, not found in the other systems. The possibility of testing the theoretical ideas in laboratory systems was the most innovative issue.

'This book presents a timely set of academic and intellectual views on Salam’s scientific passion, contribution and personality, and will be of great interest to academics in the fields of particle physics, high energy physics and scientific history of the developing world.'Contemporary PhysicsIn honor of one of the most prolific and exciting scientists of the second half of the last century, a memorial meeting was organized by the Institute of Advanced Studies at Nanyang Technological University for Professor Abdus Salam's 90th Birthday in January 2016.Salam believed that 'scientific thought is the common heritage of all mankind' and that the developing world should play its part, not merely by importing technology but by being the arbiter of its own scientific destiny. That belief saw him rise from humble beginnings in a village in Pakistan to become one of the world's most original and influential particle physicists, culminating in the 1979 Nobel Prize (shared with Glashow and Weinberg) for contributions to electroweak unification, which forms an integral part of the Standard Model.The book collected the papers presented at this memorable event which saw many distinguished scientists participating as speakers to reflect on Prof Salam's great passion for the science and achievements.

Recent experimental evidence about the possibility of "absolute negative temperature" states in physical systems has triggered a stimulating debate about the consistency of such a concept from the point of view of Statistical Mechanics. It is not clear whether the usual results of this field can be safely extended to negative-temperature states; some authors even propose fundamental modifications to the Statistical Mechanics formalism, starting with the very definition of entropy, in order to avoid the occurrence of negative values of the temperature tout-court. The research presented in this thesis aims to shed some light on this controversial topic. To this end, a particular class of Hamiltonian systems with bounded kinetic terms, which can assume negative temperature, is extensively studied, both analytically and numerically. Equilibrium and out-of-equilibrium properties of this kind of system are investigated, reinforcing the overall picture that the introduction of negative temperature does not lead to any contradiction or paradox.

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