Introduction to modern statistical mechanics

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Introduction to modern statistical mechanics

01 Jan 1987-

TL;DR: In this paper, the fundamentals conditions for equilibrium and stability of non-equilibrium systems are defined. And the Monte Carlo method in statistical mechanics is used for non-interacting (ideal) systems.

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Abstract: Thermodynamics, fundamentals conditions for equilibrium and stability statistical mechanics non-interacting (ideal) systems statistical mechanical theory of phase transitions Monte Carlo method in statistical mechanics classical fluids statistical mechanics of non-equilibrium systems.

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Nonequilibrium Equality for Free Energy Differences

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Christopher Jarzynski¹•Institutions (1)

University of Washington¹

07 Apr 1997-Physical Review Letters

TL;DR: In this paper, an expression for the equilibrium free energy difference between two configurations of a system, in terms of an ensemble of finite-time measurements of the work performed in parametrically switching from one configuration to the other, is derived.

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Abstract: An expression is derived for the equilibrium free energy difference between two configurations of a system, in terms of an ensemble of finite-time measurements of the work performed in parametrically switching from one configuration to the other. Two well-known identities emerge as limiting cases of this result.

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4,496 citations

Cites methods from "Introduction to modern statistical ..."

...io immediately reduce to Z1/Z0 (= exp−β∆F). Note that the inequality W ≥ ∆F (Eq.1) follows directly from the equality exp−βW = exp−β∆F (Eq.2a), by application of the mathematical identity expx ≥ expx [6]. This establishes W ≥ ∆F directly from a microscopic, Hamiltonian basis, rather than by invoking the increase of entropy. (In the limit t s → 0, we have W = h∆Hi0, and Eq.1 reduces to the Gibbs-Bogol...
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Graphical Models, Exponential Families, and Variational Inference

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Martin J. Wainwright¹, Michael I. Jordan¹•Institutions (1)

University of California, Berkeley¹

16 Dec 2008

TL;DR: The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.

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Abstract: The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building large-scale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide variety of algorithms — among them sum-product, cluster variational methods, expectation-propagation, mean field methods, max-product and linear programming relaxation, as well as conic programming relaxations — can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.

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4,335 citations

Cites methods from "Introduction to modern statistical ..."

...We begin with the Ising model from statistical physics [6, 20, 83], which is a particular kind of Markov random eld....
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Journal Article•DOI•

Interfaces and the driving force of hydrophobic assembly

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David Chandler¹•Institutions (1)

University of California, Berkeley¹

29 Sep 2005-Nature

TL;DR: The hydrophobic effect — the tendency for oil and water to segregate — is important in diverse phenomena, from the cleaning of laundry to the creation of micro-emulsions to make new materials, to the assembly of proteins into functional complexes.

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Abstract: The hydrophobic effect — the tendency for oil and water to segregate — is important in diverse phenomena, from the cleaning of laundry, to the creation of micro-emulsions to make new materials, to the assembly of proteins into functional complexes. This effect is multifaceted depending on whether hydrophobic molecules are individually hydrated or driven to assemble into larger structures. Despite the basic principles underlying the hydrophobic effect being qualitatively well understood, only recently have theoretical developments begun to explain and quantify many features of this ubiquitous phenomenon.

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3,162 citations

Journal Article•DOI•

Evolutionary games on graphs

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György Szabó, Gábor Fáth

01 Jul 2007-Physics Reports

TL;DR: The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.

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2,548 citations

Cites background or methods from "Introduction to modern statistical ..."

...croscopic state where the entropy S = − X s P(s)lnP(s);, (87) reaches its maximum, if the average energy is ﬁxed. The mathematical details of this approach are well described in many books [see e.g., Chandler (1987); Haken (1988)]. Glauber dynamics, as introduced above, deﬁnes a simple stochastic rule whose limit distribution (equilibrium) turns out to be the Boltzmann distribution. In the following we will show...
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...Consequently, for certain types of dynamical rules, evolutionary potential games become equivalent to manyparticle systems, whose investigations by the tools of statistical physics are very successful [for a textbook see e.g. Chandler (1987)]....
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...ypes of dynamical rules, evolutionary potential games become equivalent to many-particle systems, whose investigations by the tools of statistical physics are very successful [for a textbook see e.g. Chandler (1987)]. The exploration of the possible dynamic update rules has resulted in an extremely wide variety of models, which cannot be surveyed completely. In the following, we focus our attention on some of th...
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...The mathematical details of this approach are well described in many books [see e.g., Chandler (1987); Haken (1988)]....
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Journal Article•DOI•

Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences

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Gavin E. Crooks¹•Institutions (1)

University of California, Berkeley¹

01 Sep 1999-Physical Review E

TL;DR: A generalized version of the fluctuation theorem is derived for stochastic, microscopically reversible dynamics and this generalized theorem provides a succinct proof of the nonequilibrium work relation.

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Abstract: There are only a very few known relations in statistical dynamics that are valid for systems driven arbitrarily far-from-equilibrium. One of these is the fluctuation theorem, which places conditions on the entropy production probability distribution of nonequilibrium systems. Another recently discovered far from equilibrium expression relates nonequilibrium measurements of the work done on a system to equilibrium free energy differences. In this paper, we derive a generalized version of the fluctuation theorem for stochastic, microscopically reversible dynamics. Invoking this generalized theorem provides a succinct proof of the nonequilibrium work relation.

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Introduction to modern statistical mechanics

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