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Nonequilibrium Statistical Physics of Small Systems

Nonequilibrium Statistical Physics of Small Systems Author Rainer Klages
ISBN-10 9783527658725
Release 2013-03-15
Pages 450
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This book offers a comprehensive picture of nonequilibrium phenomena in nanoscale systems. Written by internationally recognized experts in the field, this book strikes a balance between theory and experiment, and includes in-depth introductions to nonequilibrium fluctuation relations, nonlinear dynamics and transport, single molecule experiments, and molecular diffusion in nanopores. The authors explore the application of these concepts to nano- and biosystems by cross-linking key methods and ideas from nonequilibrium statistical physics, thermodynamics, stochastic theory, and dynamical systems. By providing an up-to-date survey of small systems physics, the text serves as both a valuable reference for experienced researchers and as an ideal starting point for graduate-level students entering this newly emerging research field.

Thermodynamics of Information Processing in Small Systems

Thermodynamics of Information Processing in Small Systems Author Takahiro Sagawa
ISBN-10 9784431541684
Release 2012-09-14
Pages 120
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This thesis presents a general theory of nonequilibrium thermodynamics for information processing. Ever since Maxwell's demon was proposed in the nineteenth century, the relationship between thermodynamics and information has attracted much attention because it concerns the foundation of the second law of thermodynamics. From the modern point of view, Maxwell's demon is formulated as an information processing device that performs measurement and feedback at the level of thermal fluctuations. By unifying information theory, measurement theory, and the recently developed theory of nonequilibrium statistical mechanics, the author has constructed a theory of "information thermodynamics," in which information contents and thermodynamic variables are treated on an equal footing. In particular, the maximum work that can be extracted by the demon and the minimum work that is needed for measurement and information erasure by the demon has been determined. Additionally, generalizations of nonequilibrium relations such as a Jarzynski equality for classical stochastic systems in the presence of feedback control have been derived. One of the generalized equalities has recently been verified experimentally by using sub-micron colloidal particles. The results obtained serve as fundamental principles for information processing in small thermodynamic systems, and are applicable to nanomachines and nanodevices.

Thermodynamics and Statistical Mechanics of Small Systems

Thermodynamics and Statistical Mechanics of Small Systems Author Andrea Puglisi
ISBN-10 9783038970576
Release 2018-09-04
Pages 334
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This book is a printed edition of the Special Issue "Thermodynamics and Statistical Mechanics of Small Systems" that was published in Entropy

Nonequilibrium Statistical Physics

Nonequilibrium Statistical Physics Author Roberto Livi
ISBN-10 9781108364041
Release 2017-10-05
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Statistical mechanics has been proven to be successful at describing physical systems at thermodynamic equilibrium. Since most natural phenomena occur in nonequilibrium conditions, the present challenge is to find suitable physical approaches for such conditions: this book provides a pedagogical pathway that explores various perspectives. The use of clear language, and explanatory figures and diagrams to describe models, simulations and experimental findings makes the book a valuable resource for undergraduate and graduate students, and also for lecturers organizing teaching at varying levels of experience in the field. Written in three parts, it covers basic and traditional concepts of nonequilibrium physics, modern aspects concerning nonequilibrium phase transitions, and application-orientated topics from a modern perspective. A broad range of topics is covered, including Langevin equations, Levy processes, directed percolation, kinetic roughening and pattern formation.

Microcanonical Thermodynamics

Microcanonical Thermodynamics Author Dieter H. E. Gross
ISBN-10 9789810242152
Release 2001
Pages 269
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Boltzmann's formula S = In(W(E) defines the microcanonical ensemble. The usual textbooks on statistical mechanics start with the microensemble but rather quickly switch to the canonical ensemble introduced by Gibbs. This has the main advantage of easier analytical calculations, but there is a price to pay -- for example, phase transitions can only be defined in the thermodynamic limit of infinite system size. The question how phase transitions show up from systems with, say, 100 particles with an increasing number towards the bulk can only be answered when one finds a way to define and classify phase transitions in small systems. This is all possible within Boltzmann's original definition of the microcanonical ensemble. Starting from Boltzmann's formula, the book formulates the microcanonical thermodynamics entirely within the frame of mechanics. This way the thermodynamic limit is avoided and the formalism applies to small as well to other nonextensive systems like gravitational ones. Phasetransitions of first order, continuous transitions, critical lines and multicritical points can be unambiguously defined by the curvature of the entropy S(E, N). Special attention is given to the fragmentation of nuclei and atomic clusters as a peculiar phase transition of small systems controlled, among others, by angular momentum. The dependence of the liquid-gas transition of small atomic clusters under prescribed pressure is treated. Thus the analogue to the bulk transition can be studied. New insights into the many facets of the many-body physics of the critical point are presented. The book also describes the microcanonical statistics of the collapse of a self-gravitating system under large angular momentum.

Statistical Mechanics of Nonequilibrium Liquids

Statistical Mechanics of Nonequilibrium Liquids Author Denis J. Evans
ISBN-10 9781483260457
Release 2013-10-22
Pages 316
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Statistical Mechanics of Nonequilibrium Liquids deals with theoretical rheology. The book discusses nonlinear response of systems and outlines the statistical mechanical theory. In discussing the framework of nonequilibrium statistical mechanics, the book explains the derivation of a nonequilibrium analogue of the Gibbsian basis for equilibrium statistical mechanics. The book reviews the linear irreversible thermodynamics, the Liouville equation, and the Irving-Kirkwood procedure. The text then explains the Green-Kubo relations used in linear transport coefficients, the linear response theory, the isothermal linear response theory, as well as the equivalence of thermostatted linear responses. The book also describes how thermostatted linear mechanical response of many-body systems can be related to equilibrium fluctuations. The text explains the procedure for calculating the linear Navier-Stokes transport coefficients through computer simulation algorithms. The book also discusses the van Kampen objection to linear response theory, the steady-state fluctuations, and the thermodynamics of steady states. The text will prove valuable for researchers in molecular chemistry, scientists, and academicians involved in advanced physics.

Non equilibrium Statistical Physics with Application to Disordered Systems

Non equilibrium Statistical Physics with Application to Disordered Systems Author Manuel Osvaldo Cáceres
ISBN-10 9783319515533
Release 2017-03-07
Pages 556
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This textbook is the result of the enhancement of several courses on non-equilibrium statistics, stochastic processes, stochastic differential equations, anomalous diffusion and disorder. The target audience includes students of physics, mathematics, biology, chemistry, and engineering at undergraduate and graduate level with a grasp of the basic elements of mathematics and physics of the fourth year of a typical undergraduate course. The little-known physical and mathematical concepts are described in sections and specific exercises throughout the text, as well as in appendices. Physical-mathematical motivation is the main driving force for the development of this text. It presents the academic topics of probability theory and stochastic processes as well as new educational aspects in the presentation of non-equilibrium statistical theory and stochastic differential equations.. In particular it discusses the problem of irreversibility in that context and the dynamics of Fokker-Planck. An introduction on fluctuations around metastable and unstable points are given. It also describes relaxation theory of non-stationary Markov periodic in time systems. The theory of finite and infinite transport in disordered networks, with a discussion of the issue of anomalous diffusion is introduced. Further, it provides the basis for establishing the relationship between quantum aspects of the theory of linear response and the calculation of diffusion coefficients in amorphous systems.

A Kinetic View of Statistical Physics

A Kinetic View of Statistical Physics Author Pavel L. Krapivsky
ISBN-10 9781139493345
Release 2010-11-18
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Aimed at graduate students, this book explores some of the core phenomena in non-equilibrium statistical physics. It focuses on the development and application of theoretical methods to help students develop their problem-solving skills. The book begins with microscopic transport processes: diffusion, collision-driven phenomena, and exclusion. It then presents the kinetics of aggregation, fragmentation and adsorption, where the basic phenomenology and solution techniques are emphasized. The following chapters cover kinetic spin systems, both from a discrete and a continuum perspective, the role of disorder in non-equilibrium processes, hysteresis from the non-equilibrium perspective, the kinetics of chemical reactions, and the properties of complex networks. The book contains 200 exercises to test students' understanding of the subject. A link to a website hosted by the authors, containing supplementary material including solutions to some of the exercises, can be found at

Non equilibrium Thermodynamics and Statistical Mechanics

Non equilibrium Thermodynamics and Statistical Mechanics Author Phil Attard
ISBN-10 9780199662760
Release 2012-10-04
Pages 462
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This title builds from basic principles to advanced techniques, and covers the major phenomena, methods, and results of time-dependent systems. It is a pedagogic introduction, a comprehensive reference manual, and an original research monograph--

Non Equilibrium Thermodynamics

Non Equilibrium Thermodynamics Author S. R. De Groot
ISBN-10 9780486153506
Release 2013-01-23
Pages 528
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Classic monograph treats irreversible processes and phenomena of thermodynamics: non-equilibrium thermodynamics. Covers statistical foundations and applications with chapters on fluctuation theory, theory of stochastic processes, kinetic theory of gases, more.

Nonequilibrium Statistical Mechanics

Nonequilibrium Statistical Mechanics Author Byung Chan Eu
ISBN-10 9789401724388
Release 2013-11-11
Pages 394
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In this monograph, nonequilibrium statistical mechanics is developed by means of ensemble methods on the basis of the Boltzmann equation, the generic Boltzmann equations for classical and quantum dilute gases, and a generalised Boltzmann equation for dense simple fluids. The theories are developed in forms parallel with the equilibrium Gibbs ensemble theory in a way fully consistent with the laws of thermodynamics. The generalised hydrodynamics equations are the integral part of the theory and describe the evolution of macroscopic processes in accordance with the laws of thermodynamics of systems far removed from equilibrium. Audience: This book will be of interest to researchers in the fields of statistical mechanics, condensed matter physics, gas dynamics, fluid dynamics, rheology, irreversible thermodynamics and nonequilibrium phenomena.

Equilibrium and Non equilibrium Statistical Mechanics

Equilibrium and Non equilibrium Statistical Mechanics Author Carolyn M. Van Vliet
ISBN-10 9789812704771
Release 2008
Pages 960
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This book encompasses our current understanding of the ensemble approach to many-body physics, phase transitions and other thermal phenomena, as well as the quantum foundations of linear response theory, kinetic equations and stochastic processes. It is destined to be a standard text for graduate students, but it will also serve the specialist-researcher in this fascinating field; some more elementary topics have been included in order to make the book self-contained.The historical methods of J Willard Gibbs and Ludwig Boltzmann, applied to the quantum description rather than phase space, are featured. The tools for computations in the microcanonical, canonical and grand-canonical ensembles are carefully developed and then applied to a variety of classical and standard quantum situations. After the language of second quantization has been introduced, strongly interacting systems, such as quantum liquids, superfluids and superconductivity, are treated in detail. For the connoisseur, there is a section on diagrammatic methods and applications.In the second part dealing with non-equilibrium processes, the emphasis is on the quantum foundations of Markovian behaviour and irreversibility via the Pauli-Van Hove master equation. Justifiable linear response expressions and the quantum-Boltzmann approach are discussed and applied to various condensed matter problems. From this basis the Onsager-Casimir relations are derived, together with the mesoscopic master equation, the Langevin equation and the Fokker-Planck truncation procedure. Brownian motion and modern stochastic problems such as fluctuations in optical signals and radiation fields briefly make the round.

Nonequilibrium Many Body Theory of Quantum Systems

Nonequilibrium Many Body Theory of Quantum Systems Author Gianluca Stefanucci
ISBN-10 9781107354579
Release 2013-03-07
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The Green's function method is one of the most powerful and versatile formalisms in physics, and its nonequilibrium version has proved invaluable in many research fields. This book provides a unique, self-contained introduction to nonequilibrium many-body theory. Starting with basic quantum mechanics, the authors introduce the equilibrium and nonequilibrium Green's function formalisms within a unified framework called the contour formalism. The physical content of the contour Green's functions and the diagrammatic expansions are explained with a focus on the time-dependent aspect. Every result is derived step-by-step, critically discussed and then applied to different physical systems, ranging from molecules and nanostructures to metals and insulators. With an abundance of illustrative examples, this accessible book is ideal for graduate students and researchers who are interested in excited state properties of matter and nonequilibrium physics.

Topics in Statistical Mechanics

Topics in Statistical Mechanics Author Brian Cowan
ISBN-10 9781911298366
Release 2005-09-14
Pages 336
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Building on the material learned by students in their first few years of study, this book presents an advanced level course on statistical and thermal physics. It begins with a review of the formal structure of statistical mechanics and thermodynamics considered from a unified viewpoint. After a brief revision of non-interacting systems, emphasis is laid on interacting systems. First, weakly interacting systems are considered, where the interest is in seeing how such interactions cause small deviations from the non-interacting case. Second, systems are examined where interactions lead to drastic changes, namely phase transitions. A number of specific examples are given, and these are unified within the Landau theory of phase transitions. The final chapter of the book looks at non-equilibrium systems and the way these evolve towards equilibrium. Here, fluctuations play a vital role, as is formalized in the Fluctuation–Dissipation theorem. Contents:The Methodology of Statistical MechanicsPractical Calculations with Ideal SystemsNon-Ideal GasesPhase TransitionsFluctuations and Dynamics Readership: Upper undergraduate and postgraduate students of statistical mechanics.

An Introduction to Stochastic Processes and Nonequilibrium Statistical Physics

An Introduction to Stochastic Processes and Nonequilibrium Statistical Physics Author Horacio S. Wio
ISBN-10 9810215711
Release 1994-01-01
Pages 217
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An Introduction to Stochastic Processes and Nonequilibrium Statistical Physics has been writing in one form or another for most of life. You can find so many inspiration from An Introduction to Stochastic Processes and Nonequilibrium Statistical Physics also informative, and entertaining. Click DOWNLOAD or Read Online button to get full An Introduction to Stochastic Processes and Nonequilibrium Statistical Physics book for free.

Perspectives and Challenges in Statistical Physics and Complex Systems for the Next Decade

Perspectives and Challenges in Statistical Physics and Complex Systems for the Next Decade Author Gandhimohan M Viswanathan
ISBN-10 9789814590150
Release 2014-03-21
Pages 348
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Statistical Physics (SP) has followed an unusual evolutionary path in science. Originally aiming to provide a fundamental basis for another important branch of Physics, namely Thermodynamics, SP gradually became an independent field of research in its own right. But despite more than a century of steady progress, there are still plenty of challenges and open questions in the SP realm. In fact, the area is still rapidly evolving, in contrast to other branches of science, which already have well defined scopes and borderlines of applicability. This difference is due to the steadily expanding number of applications, as well as ongoing improvements and revisions of concepts and methods in SP. Such particular aspects of SP lend further significance and timeliness to this book about perspectives and trends within the field. Here, the aim is to present the state-of-the-art vision of expert researchers who study SP and Complex Systems. Although a comprehensive treatment is well beyond what can be treated in a single volume, the book provides a snapshot of the field today, as well as a glimpse of where the field may be heading during the next decade. The book is aimed at graduate and advanced undergraduate physics students, as well as researchers who work with SP, Complex Systems, Computational Physics, Biological Physics and related topics. It addresses questions such as: What insights can be gained from recent advances in the study of traditional problems in SP? How can SP help us understand problems that arise in the biological sciences and in the study of complex systems? How can new problems be formulated using the ‘language’ of SP? In this way, it attempts to document partial progress in answering these and related questions. The book also commemorates the occasion of the 70th anniversary in 2011 of two important physicists and friends who dedicated their lives to the understanding of nature in general and to the development of Statistical Physics and the science of Complexity in particular: Liacir Lucena and H Eugene Stanley. Contents:Further Advances in the Analysis of Traditional Problems in Statistical Physics:Comparing Methods and Monte Carlo Algorithms at Phase Transition Regimes: A General Overview (C E Fiore)Density of States of the Ising Model in the Field (B D Stošić)A Renormalization Group Study of the Three-Color Ashkin-Teller Model on a Wheatstone Hierarchical Lattice (R Teodoro, C G Bezerra, A M Mariz, F A da Costa and J M de Araújo)Applying Virial Theorem in Continuous Potential of Two Scales (N M Barraz Jr and M C Barbosa)Elementary Statistical Models for Nematic Transitions in Liquid-Crystalline Systems (D B Liarte & S R Salinas)Phase Diagram and Layer-Thinning Transitions in Free-Standing Liquid Crystal Films (M S S Pereira, I N de Oliveira and M L Lyra)On Some Experimental Reasons for an Inhomogeneous Structure of Ambient Water on the Nanometer Length Scale (F Mallamace, C Corsaro and C Vasi)Polyamorphism and Polymorphism of a Confined Water Monolayer: Liquid-Liquid Critical Point, Liquid-Crystal and Crystal-Crystal Phase Transitions (V Bianco, O Vilanova and G Franzese)New Insights into Traditional Problems in Statistical Physics:Topological and Geometrical Aspects of Phase Transitions (F A N Santos, J A Rehn and M D Coutinho-Filho)Pacman Percolation and the Glass Transition (R Pastore, M P Ciamarra and A Coniglio)Exact Solution for a Diffusive Process on a Backbone Structure: Green Function Approach and External Force (E K Lenzi, L R da Silva, A A Tateishi, M K Lenzi and H V Ribeiro)Multifractal Surfaces: Lucena and Stanley Approaches (G Corso and D A Moreira)Applications to Biological Problems:Nanoelectronics of a DNA Molecule (E L Albuquerque, U L Fulco, E W S Caetano, V N Freire, M L Lyra and F A B F Moura)Magic Trees in Mammalians Respiration or When Evolution Selected Clever Physical Systems (B Sapoval and M Filoche)Social Distancing Strategies Against Disease Spreading (L D Valdez, C Buono, P A Macri and L A Braunstein)Non-Traditional Problems Related to Complex Systems:Thermodynamics and Kinetic Theory of Granular Materials (G M Kremer)Continuous and First-Order Jamming Transition in Crossing Pedestrian Traffic Flows (H J Hilhorst, J Cividini and C Appert-Rolland)Multiplicative Processes in Visual Cognition (H F Credidio, E N Teixeira, S D S Reis, A A Moreira and J S Andrade Jr)Search Strategy: Hedging Your Bet (M F Shlesinger) Readership: Advanced undergraduates, graduate students, researchers, academics and professionals in statistical physics, complex systems and nonlinear science. Key Features:This is the only book which brings together topics as diverse as water, random searches, percolation, and trafficNo similar titles with such diversity of themes available in the marketMost of the contributors are already well known in their fieldsKeywords:Statistical Physics;Complex Systems

Statistical Physics II

Statistical Physics II Author Ryogo Kubo
ISBN-10 9783642582448
Release 2012-12-06
Pages 279
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Statistical Physics II introduces nonequilibrium theories of statistical mechanics from the viewpoint of the fluctuation-disipation theorem. Emphasis is placed on the relaxation from nonequilibrium to equilibrium states, the response of a system to an external disturbance, and general problems involved in deriving a macroscopic physical process from more basic underlying processes. Fundamental concepts and methods are stressed, rather than the numerous individual applications.