scholarly journals Definition and Time Evolution of Correlations in Classical Statistical Mechanics

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 898 ◽  
Author(s):  
Claude Dufour
Keyword(s):  
Stochastic Systems ◽  
Distribution Functions ◽  
Continuous Variables ◽  
Molecular Systems ◽  
Dense Gases ◽  
Dilute Gas ◽  
Gas System ◽  
Variable Distribution ◽  
Three Body ◽  
Superposition Approximation

The study of dense gases and liquids requires consideration of the interactions between the particles and the correlations created by these interactions. In this article, the N-variable distribution function which maximizes the Uncertainty (Shannon’s information entropy) and admits as marginals a set of (N−1)-variable distribution functions, is, by definition, free of N-order correlations. This way to define correlations is valid for stochastic systems described by discrete variables or continuous variables, for equilibrium or non-equilibrium states and correlations of the different orders can be defined and measured. This allows building the grand-canonical expressions of the uncertainty valid for either a dilute gas system or a dense gas system. At equilibrium, for both kinds of systems, the uncertainty becomes identical to the expression of the thermodynamic entropy. Two interesting by-products are also provided by the method: (i) The Kirkwood superposition approximation (ii) A series of generalized superposition approximations. A theorem on the temporal evolution of the relevant uncertainty for molecular systems governed by two-body forces is proved and a conjecture closely related to this theorem sheds new light on the origin of the irreversibility of molecular systems. In this respect, the irreplaceable role played by the three-body interactions is highlighted.

Development of the ChIMES Force Field for Reactive Molecular Systems: Carbon Monoxide at Extreme Conditions

2019 ◽  
Author(s):  
Rebecca Lindsey ◽  
Nir Goldman ◽  
Laurence E. Fried ◽  
Sorin Bastea
Keyword(s):  
Carbon Monoxide ◽  
Molecular System ◽  
Interaction Model ◽  
System Size ◽  
Single Atom ◽  
Reactive System ◽  
Extreme Conditions ◽  
Ambient Conditions ◽  
Molecular Systems ◽  
Three Body

<p>The interatomic Chebyshev Interaction Model for Efficient Simulation (ChIMES) is based on linear combinations of Chebyshev polynomials describing explicit two- and three-body interactions. Recently, the ChIMES model has been developed and applied to a molten metallic system of a single atom type (carbon), as well as a non-reactive molecular system of two atom types at ambient conditions (water). Here, we continue application of ChIMES to increasingly complex problems through extension to a reactive system. Specifically, we develop a ChIMES model for carbon monoxide under extreme conditions, with built-in transferability to nearby state points. We demonstrate that the resulting model recovers much of the accuracy of DFT while exhibiting a 10<sup>4</sup>increase in efficiency, linear system size scalability and the ability to overcome the significant system size effects exhibited by DFT.</p>

Medicine and the Chaos Theory in Description of Individual and Particular

10.12737/5892 ◽  
2014 ◽  
Vol 21 (3) ◽  
pp. 27-35
Author(s):  
Еськов ◽  
V. Eskov ◽  
Джумагалиева ◽  
L. Dzhumagalieva ◽  
Еськов ◽  
...  
Keyword(s):  
Phase Space ◽  
Time Domain ◽  
Stochastic Systems ◽  
Distribution Functions ◽  
Continuous Change ◽  
Recording Time ◽  
Behavior Dynamics ◽  
Biomedical Systems ◽  
Present Complex ◽  
Self Organizing

The article presents three approaches (deterministic, stochastic and chaotic – self-organizing) for studying biomedical systems. The authors show that complex biosystems cann’t be described by deterministic and stochastics because of constant changing parameters xi of a state vector of such systems x=x(t). The fundamental distinguish of deterministic and stochastic systems from chaotic – self-organizing is continuous movement x(t) in phase space of states. The authors also present complex of objects which the authors have been studying for the last 30 years and which conform the type III systems. The particular features of the personalized medicine are presented, that denies possibility of identification of body state at one measurement (a point in a phase space). It is connected with the fact that there is a uniform distribution x(t) in time-domain xi which is revealed in continuous change of distribution functions f(x) for different discrete recording time-domain x(t) at all xi. The authors assert that behavior dynamics of neural networks is similar to work of neuroemulators that is terminated by certainty in quasi-attractor’s volumes.

A three-body Gaussian model of solid helium

1984 ◽  
Vol 62 (7) ◽  
pp. 683-687 ◽  
Author(s):  
Douglas P. Locke
Keyword(s):  
Ground State ◽  
Reasonable Agreement ◽  
Particle Distribution ◽  
Solid Helium ◽  
Gaussian Model ◽  
Distribution Functions ◽  
Liquid Transition ◽  
Wide Range ◽  
Three Body ◽  
Ground State Energies

A simple, analytic set of three-body models is used to calculate ground state energies and single-particle distribution functions for solid 3He and 4He. Reasonable agreement with other models and experiments over a wide range of molar bolumes (10 cm3 to the liquid transition) is demonstrated.

Modelling pair distribution functions (PDFs) of organic compounds: describing both intra- and intermolecular correlation functions in calculated PDFs

2015 ◽  
Vol 48 (1) ◽  
pp. 171-178 ◽  
Author(s):  
Dragica Prill ◽  
Pavol Juhás ◽  
Martin U. Schmidt ◽  
Simon J. L. Billinge
Keyword(s):  
Structural Models ◽  
Simple Approach ◽  
Distribution Functions ◽  
Atomic Motion ◽  
Molecular Systems ◽  
Atomic Pair ◽  
Intermolecular Distances ◽  
Supercell Model ◽  
Pair Distribution Functions ◽  
Modelling Approach

The methods currently used to calculate atomic pair distribution functions (PDFs) from organic structural models do not distinguish between the intramolecular and intermolecular distances. Owing to the stiff bonding between atoms within a molecule, the PDF peaks arising from intramolecular atom–atom distances are much sharper than those of the intermolecular atom–atom distances. This work introduces a simple approach to calculate PDFs of molecular systems without building a supercell model by using two different isotropic displacement parameters to describe atomic motion: one parameter is used for the intramolecular, the other one for intermolecular atom–atom distances. Naphthalene, quinacridone and paracetamol were used as examples. Calculations were done with theDiffPy-CMIcomplex modelling infrastructure. The new modelling approach produced remarkably better fits to the experimental PDFs, confirming the higher accuracy of this method for organic materials.

Evaluation of Boltzmann Integrals for Inelastic Collision and Radiative Processes in Monatomic Plasmas

1971 ◽  
Vol 26 (11) ◽  
pp. 1888-1896
Author(s):  
H. A. Claassen
Keyword(s):  
Cross Sections ◽  
Inelastic Collision ◽  
Distribution Functions ◽  
Linear Functions ◽  
Particle Interactions ◽  
Material Particle ◽  
Radiative Processes ◽  
Moment Approximation ◽  
Three Body ◽  
Body Recombination

Within the scope of a moment method collision integrals of the Boltzmann type are formulated and evaluated for the different excited particle states of a stationary monatomic plasma macroscopically at rest. All collision and radiative processes except the three body recombination are considered. The calculations are performed within Grad’s 8-moment approximation of the momentum distribution functions of the material particle components. Assuming axial symmetry of the differential collision cross sections the evaluation leads to linear functions of generalized Chapman-Cowling integrals for binary inelastic particle interactions and to Einstein and photoionization coefficients for the radiative processes. Simplifications are given in special and limiting cases.

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