Statistical Mechanics For Athermal Fluctuation

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Statistical Mechanics For Athermal Fluctuation

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Author : Kiyoshi Kanazawa
language : en
Publisher: Springer
Release Date : 2017-11-20

Statistical Mechanics For Athermal Fluctuation written by Kiyoshi Kanazawa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-20 with Science categories.

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.

Formulation Of Statistical Mechanics Based On Thermal Pure Quantum States

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Author : Sho Sugiura
language : en
Publisher: Springer
Release Date : 2017-10-05

Formulation Of Statistical Mechanics Based On Thermal Pure Quantum States written by Sho Sugiura and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-05 with Science categories.

This thesis introduces the concept of "thermal pure quantum (TPQ) states", which are pure quantum states in equilibrium. The author establishes a new formulation of statistical mechanics based on the TPQ states. This formulation allows us to obtain not only mechanical variables but also thermodynamic variables such as entropy and free energy from a single TPQ state. Furthermore, the formulation provides a new physical description in which all fluctuations including thermally driven ones are uniquely identified to be quantum fluctuations. The use of TPQ formulation has practical advantages in its application to numerical computations and allows for significant reduction in computation cost in numerics. For demonstration purposes, a numerical computation based on TPQ formulation is applied to a frustrated two-dimensional quantum spin model, and the result is also included in this book.

Thermodynamics And Statistical Mechanics Of Small Systems

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Author : A. Vulpiani
language : en
Publisher:
Release Date : 2018

Thermodynamics And Statistical Mechanics Of Small Systems written by A. Vulpiani and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.

A challenging frontier in modern statistical physics concerns systems with a small number of degrees of freedom, far from the thermodynamic limit. Beyond the general interest in the foundation of statistical mechanics, the relevance of this subject is due to the recent increase of resolution in the observation and manipulation of biological and man-made objects at micro- and nano-scales. A peculiar feature of small systems is the role played by fluctuations, which cannot be neglected and are responsible for many non-trivial behaviors. The study of fluctuations of thermodynamic quantities, such as energy or entropy, goes back to Einstein, Onsager, and Kubo; more recently, interest in this matter has grown with the establishment of new fluctuation-dissipation relations, and of so-called stochastic thermodynamics. This turning point has received a strong impulse from the study of systems that are far from the thermodynamic equilibrium, due to very long relaxation times, as in disordered systems, or due to the presence of external forcing and dissipation, as in granular or active matter. Applications of the thermodynamic and statistical mechanics of small systems range from molecular biology to micro-mechanics, including models of nano-transport, Brownian motors, and (living or artificial) self-propelled organisms.

An Introduction To Stochastic Thermodynamics

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Author : Naoto Shiraishi
language : en
Publisher: Springer Nature
Release Date : 2023-05-08

An Introduction To Stochastic Thermodynamics written by Naoto Shiraishi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-08 with Science categories.

This book presents the fundamentals of stochastic thermodynamics, one of the most central subjects in non-equilibrium statistical mechanics. It also explores many recent advances, e.g., in information thermodynamics, the thermodynamic uncertainty relation, and the trade-off relation between efficiency and power. The content is divided into three main parts, the first of which introduces readers to fundamental topics in stochastic thermodynamics, e.g., the basics of stochastic processes, the fluctuation theorem and its variants, information thermodynamics, and large deviation theory. In turn, parts two and three explore advanced topics such as autonomous engines (engines not controlled externally) and finite speed engines, while also explaining the key concepts from recent stochastic thermodynamics theory that are involved. To fully benefit from the book, readers only need an undergraduate-level background in statistical mechanics and quantum mechanics; no background in information theory or stochastic processes is needed. Accordingly, the book offers a valuable resource for early graduate or higher-level readers who are unfamiliar with this subject but want to keep up with the cutting-edge research in this field. In addition, the author’s vivid descriptions interspersed throughout the book will help readers grasp ‘living’ research developments and begin their own research in this field.

Thermodynamics And Statistical Mechanics Of Small Systems

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Author : Andrea Puglisi
language : en
Publisher: MDPI
Release Date : 2018-09-04

Thermodynamics And Statistical Mechanics Of Small Systems written by Andrea Puglisi and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-04 with Mathematics categories.

This book is a printed edition of the Special Issue "Thermodynamics and Statistical Mechanics of Small Systems" that was published in Entropy

Equilibrium Statistical Physics

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Author : M. Baus
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-15

Equilibrium Statistical Physics written by M. Baus and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-15 with Science categories.

This is a textbook which gradually introduces the student to the statistical mechanical study of the different phases of matter and to the phase transitions between them. Throughout, only simple models of both ordinary and soft matter are used but these are studied in full detail. The subject is developed in a pedagogical manner, starting from the basics, going from the simple ideal systems to the interacting systems, and ending with the more modern topics. The textbook provides the student with a complete overview, intentionally at an introductory level, of the theory of phase transitions. All equations and deductions are included.

Statistical Mechanics

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Author : A. J. Berlinsky
language : en
Publisher: Springer Nature
Release Date : 2019-10-03

Statistical Mechanics written by A. J. Berlinsky and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-03 with Science categories.

In a comprehensive treatment of Statistical Mechanics from thermodynamics through the renormalization group, this book serves as the core text for a full-year graduate course in statistical mechanics at either the Masters or Ph.D. level. Each chapter contains numerous exercises, and several chapters treat special topics which can be used as the basis for student projects. The concept of scaling is introduced early and used extensively throughout the text. At the heart of the book is an extensive treatment of mean field theory, from the simplest decoupling approach, through the density matrix formalism, to self-consistent classical and quantum field theory as well as exact solutions on the Cayley tree. Proceeding beyond mean field theory, the book discusses exact mappings involving Potts models, percolation, self-avoiding walks and quenched randomness, connecting various athermal and thermal models. Computational methods such as series expansions and Monte Carlo simulations are discussed, along with exact solutions to the 1D quantum and 2D classical Ising models. The renormalization group formalism is developed, starting from real-space RG and proceeding through a detailed treatment of Wilson’s epsilon expansion. Finally the subject of Kosterlitz-Thouless systems is introduced from a historical perspective and then treated by methods due to Anderson, Kosterlitz, Thouless and Young. Altogether, this comprehensive, up-to-date, and engaging text offers an ideal package for advanced undergraduate or graduate courses or for use in self study.

Equilibrium Statistical Physics

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Author : Marc Baus
language : en
Publisher: Springer Nature
Release Date : 2021-06-04

Equilibrium Statistical Physics written by Marc Baus and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-04 with Science categories.

This is a textbook which gradually introduces the student to the statistical mechanical study of the different phases of matter and to the phase transitions between them. Throughout, only simple models of both ordinary and soft matter are used but these are studied in full detail. The subject is developed in a pedagogical manner, starting from the basics, going from the simple ideal systems to the interacting systems, and ending with the more modern topics. The textbook provides the student with a complete overview, intentionally at an introductory level, of the theory of phase transitions. All equations and deductions are included.

Equilibrium Statistical Physics

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Author : Michael Plischke
language : en
Publisher: World Scientific
Release Date : 1994

Equilibrium Statistical Physics written by Michael Plischke and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Science categories.

This textbook concentrates on modern topics in statistical physics with an emphasis on strongly interacting condensed matter systems. The book is self-contained and is suitable for beginning graduate students in physics and materials science or undergraduates who have taken an introductory course in statistical mechanics. Phase transitions and critical phenomena are discussed in detail including mean field and Landau theories and the renormalization group approach. The theories are applied to a number of interesting systems such as magnets, liquid crystals, polymers, membranes, interacting Bose and Fermi fluids; disordered systems, percolation and spin of equilibrium concepts are also discussed. Computer simulations of condensed matter systems by Monte Carlo-based and molecular dynamics methods are treated.

Noise And Fluctuations

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Author : D. K. C. MacDonald
language : en
Publisher: Courier Corporation
Release Date : 2006-01-01

Noise And Fluctuations written by D. K. C. MacDonald and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-01 with Science categories.

An understanding of fluctuations and their role is both useful and fundamental to the study of physics. This concise study of random processes offers graduate students and research physicists a survey that encompasses both the relationship of Brownian Movement with statistical mechanics and the problem of irreversible processes. It outlines the basics of the physics involved, without the strictures of mathematical rigor. The three-part treatment starts with a general survey of Brownian Movement, including electrical Brownian Movement and "shot-noise," Part two explores correlation, frequency spectrum, and distribution function, with particular focus on application to Brownian Movement. The final section examines noise in electric currents, including noise in vacuum tubes and a random rectangular current. Frequent footnotes amplify the text, along with an extensive selection of Appendixes.