..., such as proteins in specific applications, and we provide a comprehensive toolkit for the exploration of molecular energy landscapes with neural networks. molecular dynamics Boltzmann generator rotameric sampling differentiable programming neural network statistical mechanics National Institutes of Health...

...) by using the following equation: (5) where q_h is the highest q value within S_exp(q). We note that it is also able to calculate the sum of squared residual using the corresponding total correlation functions. Statistical mechanics of simple liquids...

.../pages/about_us/legal/notices ) Abstract I highlight that the aim of using statistical mechanics to underpin irreversible processes is, strictly speaking, ambiguous. Traditionally, however, the task of underpinning irreversible processes has been thought to be synonymous with underpinning the Second Law...

..., the Boltzmann distribution from classical statistical mechanics can be used to predict the network properties of time-evolving networks [ 33 ]. Tools from statistical mechanics can also be used to characterize the degree distribution for different types of complex networks [ 3 ]. Furthermore, by using a heat...

... of statistical mechanics are related, in that equilibrium can be achieved by constraining the forward and backward rates K_IJ and K_JI so as to satisfy the condition of ‘detailed balance’ ( for some ). This implies a steady state for a Boltzmann distribution defined...

... statistics and observe that symplectic Euler performs significantly better than the others for comparable computational expense. equations and systems with randomness; Hamiltonian systems; statistical mechanics; symplectic numerical methods Received on 18 March 2003. revised on 1 June 2004. ...

...Simanchal Padhy 29 3 2004 30 3 2004 © 2004 RAS 2004 Summary The statistics of the Bhuj earthquake population are examined to investigate the proximity of the system to the critical state, defined through an entropy-energy relationship based on the tools of statistical mechanics...

... of protein chains from their amino acid sequences. The approach is based on the use of the self-consistent molecular field theory for long-range interactions, the use of 1-D statistical mechanics for short-range interactions and on the discovery that there is and should only be a relatively small discrete...

.... Nearest neighbour Points on a sphere Statistical mechanics. 466 Miscellanea Biometrika (1980), 67, 2, pp. 466-9 Printed in Great Britain Further bounds for the distribution of minimum interpoint distance on a sphere BY DAVID J. GATES AND MARK WESTCOTT CSIRO...

... (fundamentals, many-particle systems and the occupation number representation). (4) Thermodynamics and statistical mechanics (thermodynamics, statistical mechanics, quantum distributions, coarse graining). (5) Physical observables as random variables (origin of randomness in physical systems, joint...

... we look first at what we mean by statistical physics, giving a brief overview of the discipline we call statistical mechanics. Whole books have been written on statistical mechanics, and our synopsis takes only a few pages, so we must necessarily deal only with the very basics of the subject. We...

... the theory of photoelectricity, created a new statistical mechanics by studying Brownian motion, gave a fully formed theory of special relativity, and derived his famous mass-energy equation. This monumental accomplishment was matched only by Newton's work during the plague years. A decade later, Einstein...

...This chapter analyzes permutation symmetry, focusing on the proper understanding of pchapter indistinguishability in classical statistical mechanics and in quantum theory. It shows that it is possible to treat the statistical mechanical statistics for classical pchapters as invariant under...

..., may be expressed as partition functions of exactly solved models in statistical mechanics. The transition to ice-type models represents a subtle shift in emphasis from the crystal basis representation, and suggests the introduction of a new tool, the Yang-Baxter equation. This tool was developed...

... Boundary conditions Helmholtz free energy canonical partition function spatial distribution function van der Waals equation Henderson Theorem non-Hamiltonian statistical mechanics Nosé Hamiltonian Nosé-Hoover chains isokinetic ensemble resonance-free molecular dynamics The microcanonical...

... Equilibrium classical statistical mechanics field theory auxiliary field polymer copolymer electrostatic interaction supramolecular coherent state The previous chapter showcased examples of molecularly-informed field theory models based on an underlying coarse-grained particle description. We have...

... peptide protein vii activation function cross entropy lasso regression regularisation conditional probability Markov process transition matrix Supervised learning Classification Perceptron Support vector machines Generalisation Multilayer neural network Statistical mechanics of learning...

... objects (in closed systems), never the reverse. More generally, systems spontaneously move from non-equilibrium states to equilibrium states, never the reverse. Delving into the foundations of statistical mechanics, this chapter reviews the many open questions in that field as they relate to temporal...

... that subjectivism provides a viable interpretation of probabilities in statistical mechanics. However, claims to the effect that subjectivism can overcome problems with more objectivist interpretations are rejected. In particular, Jaynes' argument for the Second Law of Thermodynamics is found wanting...

...Fig. 1. The ergodic decomposition of Γ, where Γ₁, …, Γ₅ are Lebesgue‐indecomposable. This chapter defends and refines a specific objectivist interpretation of probabilities in statistical mechanics. For ergodic systems, probabilities are defined as time-averages. For other...