Stochastic Energetics by now commonly designates the emerging field that bridges the gap between stochastic dynamical processes and thermodynamics. Triggered by the vast improvements in spatio-temporal resolution in nanotechnology, stochastic energetics develops a framework for quantifying individual realizations of a stochastic process on the mesoscopic scale of thermal fluctuations. This is needed to answer such novel questions as: Can one cool a drop of water by agitating an immersed nano-particle? How does heat flow if a Brownian particle pulls a polymer chain? Can one measure the free-energy of a system through a single realization of the associated stochastic process? This book will take the reader gradually from the basics to the applications: Part I provides the necessary background from stochastic dynamics (Langevin, master equation), Part II introduces how stochastic energetics describes such basic notions as heat and work on the mesoscopic scale, Part III details several applications, such as control and detection processes, as well as free-energy transducers. It aims in particular at researchers and graduate students working in the fields of nanoscience and technology.

This thesis both broadens and deepens our understanding of the Brownian world. It addresses new problems in diffusion theory that have recently attracted considerable attention, both from the side of nanotechnology and from the viewpoint of pure academic research. The author focusses on the difussion of interacting particles in restricted geometries and under externally controlled forces. These geometries serve, for example, to model ion transport through narrow channels in cell membranes or a Brownian particle diffusing in an optical trap, now a paradigm for both theory and experiment. The work is exceptional in obtaining explicit analytically formulated answers to such realistic, experimentally relevant questions. At the same time, with its detailed exposition of the problems and a complete set of references, it presents a clear and broadly accessible introduction to the domain. Many of the problem settings and the corresponding exact asymptotic laws are completely new in diffusion theory.

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

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.

The nonequilibrium behavior of nanoscopic and biological systems, which are typically strongly fluctuating, is a major focus of current research. Lately, much progress has been made in understanding such systems from a thermodynamic perspective. However, new theoretical challenges emerge when the fluctuating system is additionally subject to time delay, e.g. due to the presence of feedback loops. This thesis advances this young and vibrant research field in several directions. The first main contribution concerns the probabilistic description of time-delayed systems; e.g. by introducing a versatile approximation scheme for nonlinear delay systems. Second, it reveals that delay can induce intriguing thermodynamic properties such as anomalous (reversed) heat flow. More generally, the thesis shows how to treat the thermodynamics of non-Markovian systems by introducing auxiliary variables. It turns out that delayed feedback is inextricably linked to nonreciprocal coupling, information flow, and to net energy input on the fluctuating level.

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.

The first comprehensive graduate-level introduction to stochastic thermodynamics Stochastic thermodynamics is a well-defined subfield of statistical physics that aims to interpret thermodynamic concepts for systems ranging in size from a few to hundreds of nanometers, the behavior of which is inherently random due to thermal fluctuations. This growing field therefore describes the nonequilibrium dynamics of small systems, such as artificial nanodevices and biological molecular machines, which are of increasing scientific and technological relevance. This textbook provides an up-to-date pedagogical introduction to stochastic thermodynamics, guiding readers from basic concepts in statistical physics, probability theory, and thermodynamics to the most recent developments in the field. Gradually building up to more advanced material, the authors consistently prioritize simplicity and clarity over exhaustiveness and focus on the development of readers’ physical insight over mathematical formalism. This approach allows the reader to grow as the book proceeds, helping interested young scientists to enter the field with less effort and to contribute to its ongoing vibrant development. Chapters provide exercises to complement and reinforce learning. Appropriate for graduate students in physics and biophysics, as well as researchers, Stochastic Thermodynamics serves as an excellent initiation to this rapidly evolving field. Emphasizes a pedagogical approach to the subject Highlights connections with the thermodynamics of information Pays special attention to molecular biophysics applications Privileges physical intuition over mathematical formalism Solutions manual available on request for instructors adopting the book in a course

The essential introduction to modern statistical mechanics—now completely updated and expanded Statistical mechanics is one of the most exciting areas of physics today and has applications to subjects ranging from economics and social behavior to algorithmic theory and evolutionary biology. Statistical Mechanics in a Nutshell provides a self-contained introduction to this rapidly developing field. Starting with the basics of kinetic theory and requiring only a background in elementary calculus and mechanics, this concise book discusses the most important developments of recent decades and guides readers to the very threshold of today’s cutting-edge research. Features a new chapter on stochastic thermodynamics with an introduction to the thermodynamics of information—the first treatment of its kind in an introductory textbook Offers a more detailed account of numerical simulations, including simulated annealing and other accelerated Monte Carlo methods The chapter on complex systems now features an accessible introduction to the replica theory of spin glasses and the Hopfield theory of neural networks, with an emphasis on applications Provides a new discussion of defect-mediated transitions and their implications for two-dimensional melting An invaluable resource for graduate students and advanced undergraduates seeking a compact primer on the core ideas of statistical mechanics Solutions manual (available only to instructors)

This book provides a comprehensive and self-contained overview of recent progress in nonequilibrium statistical mechanics, in particular, the discovery of fluctuation relations and other time-reversal symmetry relations. The significance of these advances is that nonequilibrium statistical physics is no longer restricted to the linear regimes close to equilibrium, but extends to fully nonlinear regimes. These important new results have inspired the development of a unifying framework for describing both the microscopic dynamics of collections of particles, and the macroscopic hydrodynamics and thermodynamics of matter itself. The book discusses the significance of this theoretical framework in relation to a broad range of nonequilibrium processes, from the nanoscale to the macroscale, and is essential reading for researchers and graduate students in statistical physics, theoretical chemistry and biological physics.

This thesis reveals how the feedback trap technique, developed to trap small objects for biophysical measurement, could be adapted for the quantitative study of the thermodynamic properties of small systems. The experiments in this thesis are related to Maxwell’s demon, a hypothetical intelligent, “neat fingered” being that uses information to extract work from heat, apparently creating a perpetual-motion machine. The second law of thermodynamics should make that impossible, but how? That question has stymied physicists and provoked debate for a century and a half. The experiments in this thesis confirm a hypothesis proposed by Rolf Landauer over fifty years ago: that Maxwell’s demon would need to erase information, and that erasing information—resetting the measuring device to a standard starting state—requires dissipating as much energy as is gained. For his thesis work, the author used a “feedback trap” to study the motion of colloidal particles in “v irtual potentials” that may be manipulated arbitrarily. The feedback trap confines a freely diffusing particle in liquid by periodically measuring its position and applying an electric field to move it back to the origin.