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A Kinetic View of Statistical Physics

TL;DR: In this paper, the authors focus on the development and application of theoretical methods to help students develop their problem-solving skills in non-equilibrium statistical physics, and present 200 exercises to test students' understanding of the subject.
Abstract: 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 www.cambridge.org/9780521851039.

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Journal ArticleDOI
TL;DR: The eigenstate thermalization hypothesis (ETH) as discussed by the authors is a natural extension of quantum chaos and random matrix theory (RMT) that allows one to describe thermalization in isolated chaotic systems without invoking the notion of an external bath.
Abstract: This review gives a pedagogical introduction to the eigenstate thermalization hypothesis (ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first part, ETH is introduced as a natural extension of ideas from quantum chaos and random matrix theory (RMT). To this end, we present a brief overview of classical and quantum chaos, as well as RMT and some of its most important predictions. The latter include the statistics of energy levels, eigenstate components, and matrix elements of observables. Building on these, we introduce the ETH and show that it allows one to describe thermalization in isolated chaotic systems without invoking the notion of an external bath. We examine numerical evidence of eigenstate thermalization from studies of many-body lattice systems. We also introduce the concept of a quench as a means of taking isolated systems out of equilibrium, and discuss results of numerical experiments on quantum quenches. The second part of the review explores the i...

1,536 citations

Journal ArticleDOI
TL;DR: A selective overview of the fast-developing field of MIPS, focusing on theory and effects, is given, which generally breaks down at higher order in gradients.
Abstract: Self-propelled particles include both self-phoretic synthetic colloids and various microorganisms. By continually consuming energy, they bypass the laws of equilibrium thermodynamics. These laws enforce the Boltzmann distribution in thermal equilibrium: The steady state is then independent of kinetic parameters. In contrast, self-propelled particles tend to accumulate where they move more slowly. They may also slow down at high density for either biochemical or steric reasons. This creates positive feedback, which can lead to motility-induced phase separation (MIPS) between dense and dilute fluid phases. At leading order in gradients, a mapping relates variable-speed, self-propelled particles to passive particles with attractions. This deep link to equilibrium phase separation is confirmed by simulations but generally breaks down at higher order in gradients: New effects, with no equilibrium counterpart, then emerge. We give a selective overview of the fast-developing field of MIPS, focusing on theory and...

1,228 citations

Journal ArticleDOI
TL;DR: The eigenstate thermalization hypothesis (ETH) as mentioned in this paper is a natural extension of quantum chaos and random matrix theory (RMT) and it allows one to describe thermalization in isolated chaotic systems without invoking the notion of an external bath.
Abstract: This review gives a pedagogical introduction to the eigenstate thermalization hypothesis (ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first part, ETH is introduced as a natural extension of ideas from quantum chaos and random matrix theory (RMT). To this end, we present a brief overview of classical and quantum chaos, as well as RMT and some of its most important predictions. The latter include the statistics of energy levels, eigenstate components, and matrix elements of observables. Building on these, we introduce the ETH and show that it allows one to describe thermalization in isolated chaotic systems without invoking the notion of an external bath. We examine numerical evidence of eigenstate thermalization from studies of many-body lattice systems. We also introduce the concept of a quench as a means of taking isolated systems out of equilibrium, and discuss results of numerical experiments on quantum quenches. The second part of the review explores the implications of quantum chaos and ETH to thermodynamics. Basic thermodynamic relations are derived, including the second law of thermodynamics, the fundamental thermodynamic relation, fluctuation theorems, and the Einstein and Onsager relations. In particular, it is shown that quantum chaos allows one to prove these relations for individual Hamiltonian eigenstates and thus extend them to arbitrary stationary statistical ensembles. We then show how one can use these relations to obtain nontrivial universal energy distributions in continuously driven systems. At the end of the review, we briefly discuss the relaxation dynamics and description after relaxation of integrable quantum systems, for which ETH is violated. We introduce the concept of the generalized Gibbs ensemble, and discuss its connection with ideas of prethermalization in weakly interacting systems.

985 citations


Cites background from "A Kinetic View of Statistical Physi..."

  • ...By doing that, one recovers the detailed balance condition in its most familiar form [211]: pI(nI → mI) pI(mI → nI) ≈ e −βII(EII)δEI mn , (166)...

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Journal ArticleDOI
TL;DR: It is argued that conceptual unification across ecology, genetics, evolution and physiology has fostered even more fertile questions that have far reaching implications for the understanding of how ecosystem function and biodiversity will withstand environmental changes in the 21st century.
Abstract: Over the past 20 years, major advances have clarified how ecological patterns inform theory, and how in turn theory informs applied ecology. Also, there has been an increased recognition that the problem of scale at which ecological processes should be considered is critical if we are to produce general predictions. Ecological dynamics is always stochastic at small scales, but variability is conditional on the scale of description. The radical changes in the scope and aims of ecology over the past decades reflect in part the need to address pressing societal issues of environmental change. Technological advances in molecular biology, global positioning, sensing instrumentation and computational power should not be overlooked as an explanation for these radical changes. However, I argue that conceptual unification across ecology, genetics, evolution and physiology has fostered even more fertile questions. We are moving away from the view that evolution is played in a fixed ecological theatre: the theatre is being rapidly and relentlessly redesigned by the players themselves. The maintenance of ecosystem functions depends on shifts in species assemblages and on cellular metabolism, not only on flows of energy and matter. These findings have far reaching implications for our understanding of how ecosystem function and biodiversity will withstand (or not) environmental changes in the 21st century.

862 citations


Cites background from "A Kinetic View of Statistical Physi..."

  • ...7 illustrates two generic models of spatial patterning (the voter model and the zero-temperature Ising model, see Krapivsky et al. 2010) where the local rules combined with the information exchange between nearest neighbours generate a macroscopic pattern (see more details in the Appendix S1)....

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Journal ArticleDOI
TL;DR: All these approaches to genetic analysis using networks are variations of a unifying mathematical machinery — network propagation — suggesting that it is a powerful data transformation method of broad utility in genetic research.
Abstract: Biological networks are powerful resources for the discovery of genes and genetic modules that drive disease. Fundamental to network analysis is the concept that genes underlying the same phenotype tend to interact; this principle can be used to combine and to amplify signals from individual genes. Recently, numerous bioinformatic techniques have been proposed for genetic analysis using networks, based on random walks, information diffusion and electrical resistance. These approaches have been applied successfully to identify disease genes, genetic modules and drug targets. In fact, all these approaches are variations of a unifying mathematical machinery - network propagation - suggesting that it is a powerful data transformation method of broad utility in genetic research.

502 citations

References
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Book
01 Jan 2001
TL;DR: The paradoxes of irreversibility as mentioned in this paper is a well-known problem in nonlinear problems, and it has been studied extensively in the literature for a long time, e.g. in the context of projection operators.
Abstract: 1. Brownian Motion and Langevin equations 2. Fokker-Planck equations 3. Master equations 4. Reaction rates 5. Kinetic models 6. Quantum dynamics 7. Linear response theory 8. Projection operators 9. Nonlinear problems 10. The paradoxes of irreversibility Appendices

2,050 citations

BookDOI
01 Jan 1998

65 citations