Nonequilibrium Equality for Free Energy Differences
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.
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.
Citations
More filters
Book•
[...]
TL;DR: Deep learning as mentioned in this paper is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts, and it is used in many applications such as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames.
Abstract: Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.
38,208 citations
TL;DR: NAMD as discussed by the authors is a parallel molecular dynamics code designed for high-performance simulation of large biomolecular systems that scales to hundreds of processors on high-end parallel platforms, as well as tens of processors in low-cost commodity clusters, and also runs on individual desktop and laptop computers.
Abstract: NAMD is a parallel molecular dynamics code designed for high-performance simulation of large biomolecular systems. NAMD scales to hundreds of processors on high-end parallel platforms, as well as tens of processors on low-cost commodity clusters, and also runs on individual desktop and laptop computers. NAMD works with AMBER and CHARMM potential functions, parameters, and file formats. This article, directed to novices as well as experts, first introduces concepts and methods used in the NAMD program, describing the classical molecular dynamics force field, equations of motion, and integration methods along with the efficient electrostatics evaluation algorithms employed and temperature and pressure controls used. Features for steering the simulation across barriers and for calculating both alchemical and conformational free energy differences are presented. The motivations for and a roadmap to the internal design of NAMD, implemented in C++ and based on Charm++ parallel objects, are outlined. The factors affecting the serial and parallel performance of a simulation are discussed. Finally, typical NAMD use is illustrated with representative applications to a small, a medium, and a large biomolecular system, highlighting particular features of NAMD, for example, the Tcl scripting language. The article also provides a list of the key features of NAMD and discusses the benefits of combining NAMD with the molecular graphics/sequence analysis software VMD and the grid computing/collaboratory software BioCoRE. NAMD is distributed free of charge with source code at www.ks.uiuc.edu.
14,558 citations
Cites background or methods from "Nonequilibrium Equality for Free En..."
...The Jarzynski equality provides a way to extract equilibrium information, such as free energy differences, from averaging over nonequilibrium processes,76 a method that has been tested against computer simulations77 and experiments.78 A major difficulty that arises with the application of eq....
[...]
...The Jarzynski equality provides a way to extract equilibrium information, such as free energy differences, from averaging over nonequilibrium processes [76], a method that has been tested against computer simulations [77] and experiments [78]....
[...]
...Cumulant expansions [76,79,62,41] are an effective approximation for the exponential average; since the lower-order terms of the expansion are less influenced by statistical error, the systematic error introduced by truncating the higher order terms may be considerably smaller than the statistical error which would be introduced by including them....
[...]
...Jarzynski76 discovered an equality that holds regardless of the speed of the process: e F e W , (19) where (kBT) 1....
[...]
...Jarzynski [76] discovered an equality that holds regardless of the speed of the process:...
[...]
TL;DR: The software suite GROMACS (Groningen MAchine for Chemical Simulation) that was developed at the University of Groningen, The Netherlands, in the early 1990s is described, which is a very fast program for molecular dynamics simulation.
Abstract: This article describes the software suite GROMACS (Groningen MAchine for Chemical Simulation) that was developed at the University of Groningen, The Netherlands, in the early 1990s. The software, written in ANSI C, originates from a parallel hardware project, and is well suited for parallelization on processor clusters. By careful optimization of neighbor searching and of inner loop performance, GROMACS is a very fast program for molecular dynamics simulation. It does not have a force field of its own, but is compatible with GROMOS, OPLS, AMBER, and ENCAD force fields. In addition, it can handle polarizable shell models and flexible constraints. The program is versatile, as force routines can be added by the user, tabulated functions can be specified, and analyses can be easily customized. Nonequilibrium dynamics and free energy determinations are incorporated. Interfaces with popular quantum-chemical packages (MOPAC, GAMES-UK, GAUSSIAN) are provided to perform mixed MM/QM simulations. The package includes about 100 utility and analysis programs. GROMACS is in the public domain and distributed (with source code and documentation) under the GNU General Public License. It is maintained by a group of developers from the Universities of Groningen, Uppsala, and Stockholm, and the Max Planck Institute for Polymer Research in Mainz. Its Web site is http://www.gromacs.org.
13,116 citations
TL;DR: An overview of the CHARMM program as it exists today is provided with an emphasis on developments since the publication of the original CHARMM article in 1983.
Abstract: CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecu- lar simulation program. It has been developed over the last three decades with a primary focus on molecules of bio- logical interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estima- tors, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numer- ous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.
7,035 citations
References
More filters
Book•
01 Jan 2010
TL;DR: In this article, a discussion of some of the basic physical concepts and methods useful in the description of situations involving systems which consist of very many particulars is presented for the junior-senior thermodynamics course given in all departments as a standard part of the curriculum.
Abstract: This book is designed for the junior-senior thermodynamics course given in all departments as a standard part of the curriculum. The book is devoted to a discussion of some of the basic physical concepts and methods useful in the description of situations involving systems which consist of very many particulars. It attempts, in particular, to introduce the reader to the disciplines of thermodynamics, statistical mechanics, and kinetic theory from a unified and modern point of view. The presentation emphasizes the essential unity of the subject matter and develops physical insight by stressing the microscopic content of the theory.
3,171 citations
Book•
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.
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.
2,510 citations
"Nonequilibrium Equality for Free En..." refers methods in this paper
...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...
[...]
01 Jan 1965
TL;DR: In this article, a discussion of some of the basic physical concepts and methods useful in the description of situations involving systems which consist of very many particulars is presented for the junior-senior thermodynamics course given in all departments as a standard part of the curriculum.
Abstract: This book is designed for the junior-senior thermodynamics course given in all departments as a standard part of the curriculum. The book is devoted to a discussion of some of the basic physical concepts and methods useful in the description of situations involving systems which consist of very many particulars. It attempts, in particular, to introduce the reader to the disciplines of thermodynamics, statistical mechanics, and kinetic theory from a unified and modern point of view. The presentation emphasizes the essential unity of the subject matter and develops physical insight by stressing the microscopic content of the theory.
1,500 citations