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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.
This book is a printed edition of the Special Issue "Thermodynamics and Statistical Mechanics of Small Systems" that was published in Entropy
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.
This book provides an introduction to topics in non-equilibrium quantum statistical physics for both mathematicians and theoretical physicists. The first part introduces a kinetic equation, of Kolmogorov type, which is needed to describe an isolated atom (actually, in experiments, an ion) under the effect of a classical pumping electromagnetic field which keeps the atom in its excited state(s) together with the random emission of fluorescence photons which put it back into its ground state. The quantum kinetic theory developed in the second part is an extension of Boltzmann's classical (non-quantum) kinetic theory of a dilute gas of quantum bosons. This is the source of many interesting fundamental questions, particularly because, if the temperature is low enough, such a gas is known to have at equilibrium a transition, the Bose–Einstein transition, where a finite portion of the particles stay in the quantum ground state. An important question considered is how a Bose gas condensate develops in time if its energy is initially low enough.
This self-contained volume introduces modern methods of statistical mechanics in turbulence, with three harmonised lecture courses by world class experts.
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.
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.
This text on the statistical theory of nonequilibrium phenomena grew out of lecture notes for courses on advanced statistical mechanics that were held more or less regularly at the Physics Department of the Technical University in Munich. My aim in these lectures was to incorporate various developments of many-body theory made during the last 20-30 years, in particular the correlation function approach, not just as an "extra" alongside the more "classical" results; I tried to use this approach as a unifying concept for the presentation of older as well as more recent results. I think that after so many excellent review articles and advanced treatments, correlation functions and memory kernels are as much a matter of course in nonequilibrium statistical physics as partition functions are in equilibrium theory, and should be used as such in regular courses and textbooks. The relations between correlation functions and earlier vehicles for the formulation of nonequilibrium theory such as kinetic equations, master equations, Onsager's theory, etc. , are discussed in detail in this volume. Since today there is growing interest in nonlinear phenomena I have included several chapters on related problems. There is some nonlinear response theory, some results on phenomenological nonlinear equations and some microscopic applications of the nonlinear response formalism. The main focus, however, is on the linear regime.
Building on the material learned by students in their first few years of study, Topics in Statistical Mechanics (Second Edition) 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. There is a brief revision of non-interacting systems, including quantum gases and a discussion of negative temperatures. Following this, emphasis is on interacting systems. First, weakly interacting systems are considered, where the interest is in seeing how small 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 is given, and these are unified within the Landau theory of phase transitions. The final chapter of the book looks at non-equilibrium systems, in particular the way they evolve towards equilibrium. This is framed within the context of linear response theory. Here fluctuations play a vital role, as is formalised in the fluctuation-dissipation theorem.The second edition has been revised particularly to help students use this book for self-study. In addition, the section on non-ideal gases has been expanded, with a treatment of the hard-sphere gas, and an accessible discussion of interacting quantum gases. In many cases there are details of Mathematica calculations, including Mathematica Notebooks, and expression of some results in terms of Special Functions.
The author investigates athermal fluctuation from the viewpoints of statistical mechanics in this thesis. Stochastic methods are theoretically very powerful in describing fluctuation of thermodynamic quantities in small systems on the level of a single trajectory and have been recently developed on the basis of stochastic thermodynamics. This thesis proposes, for the first time, a systematic framework to describe athermal fluctuation, developing stochastic thermodynamics for non-Gaussian processes, while thermal fluctuations are mainly addressed from the viewpoint of Gaussian stochastic processes in most of the conventional studies. First, the book provides an elementary introduction to the stochastic processes and stochastic thermodynamics. The author derives a Langevin-like equation with non-Gaussian noise as a minimal stochastic model for athermal systems, and its analytical solution by developing systematic expansions is shown as the main result. Furthermore, the a uthor shows a thermodynamic framework for such non-Gaussian fluctuations, and studies some thermodynamics phenomena, i.e. heat conduction and energy pumping, which shows distinct characteristics from conventional thermodynamics. The theory introduced in the book would be a systematic foundation to describe dynamics of athermal fluctuation quantitatively and to analyze their thermodynamic properties on the basis of stochastic methods.