The most probable distribution in statistical thermodynamics

1971 ◽  
Vol 48 (9) ◽  
pp. 601 ◽  
Author(s):  
Robert G. Keil ◽  
Leonard K. Nash
Keyword(s):  
Statistical Thermodynamics ◽  
Probable Distribution ◽  
Most Probable Distribution

Statistical Thermodynamics Concepts and Mathematical Tools for a Multi-Agent Ecosystem

2014 ◽  
Vol 20 (2) ◽  
pp. 237-270
Author(s):  
Javier Segovia
Keyword(s):  
Statistical Mechanics ◽  
Mathematical Problem ◽  
Statistical Thermodynamics ◽  
Economic Systems ◽  
Global Behavior ◽  
Probable Distribution ◽  
Or Economics ◽  
Artificial Ecosystems ◽  
Multi Agent ◽  
Most Probable Distribution

Finding the distribution of systems over their possible states is a mathematical problem. One possible solution is the method of the most probable distribution developed by Boltzmann. This method has been instrumental in developing statistical mechanics and explaining the origin of many thermodynamics concepts, like entropy or temperature, but is also applicable in many other fields like ecology or economics. Artificial ecosystems have many features in common with ecological or economic systems, but surprisingly the method does not appear to have been very successful in this field of application. The hypothesis of this article is that this failure is due to the incorrect interpretation of the method's concepts and mathematical tools. We propose to review and reinterpret the method so that it can be correctly applied and all its potential exploited in order to study and characterize the global behavior of an artificial multi-agent ecosystem.

Application of Boltzmann Statistical Mechanics in the Validation of the Gaussian Summit-Height Distribution in Rough Surfaces

1997 ◽  
Vol 119 (4) ◽  
pp. 846-850 ◽  
Author(s):  
M. Leung ◽  
C. K. Hsieh ◽  
D. Y. Goswami
Keyword(s):  
Surface Roughness ◽  
Statistical Mechanics ◽  
Theoretical Basis ◽  
Rough Surfaces ◽  
Electrical Contact ◽  
Height Distribution ◽  
Probable Distribution ◽  
Theoretical Predictions ◽  
Most Probable Distribution ◽  
Roughness Measurements

In theoretical modeling of contact mechanics, a homogeneously, isotropically rough surface is usually assumed to be a flat plane covered with asperities of a Gaussian summit-height distribution. This assumption yields satisfactory results between theoretical predictions and experimental measurements of the physical characteristics, such as thermal/electrical contact conductance and friction coefficient. However, lack of theoretical basis of this assumption motivates further study in surface modeling. This paper presents a theoretical investigation by statistical mechanics to determine surface roughness in terms of the most probable distribution of surface asperities. Based upon the surface roughness measurements as statistical constraints, the Boltzmann statistical model derives a distribution equivalent to Gaussian. The Boltzmann statistical mechanics derivation in this paper provides a rigorous validation of the Gaussian summit-height assumption presently in use for study of rough surfaces.

Method of most probable distribution: New solutions and results

Pramana ◽  
1989 ◽  
Vol 33 (4) ◽  
pp. 455-465 ◽  
Author(s):  
V J Menon ◽  
D C Agrawal
Keyword(s):  
Probable Distribution ◽  
Most Probable Distribution

The polymerization of styrene by sulphuric acid - III. The molecular weight distribution

1961 ◽  
Vol 263 (1312) ◽  
pp. 75-81 ◽  
Keyword(s):  
Molecular Weight ◽  
Sulphuric Acid ◽  
Molecular Weight Distribution ◽  
Weight Distribution ◽  
High Conversion ◽  
Chain Growth ◽  
Characteristic Parameters ◽  
Relative Probability ◽  
Probable Distribution ◽  
Most Probable Distribution

The theory of the molecular weight distribution in polystyrenes initiated by sulphuric acid, described in part I, has been tested by preparation and fractionation of suitable low-yield polymer samples. The expected ‘most probable’ distribution is found in these samples, but not in a high-conversion polymer. The characteristic parameters of the distributions the relative probability of chain growth—agree with values calculated from the kinetic con­stants measured in part II.

STUDY ON THE MOST PROBABLE DISTRIBUTION FOR LAUGHLIN WAVE FUNCTIONS

1993 ◽  
Vol 07 (10) ◽  
pp. 679-687
Author(s):  
SHAOJIN QIN ◽  
ZHAOBIN SU ◽  
BINGSHEN WANG
Keyword(s):  
Wave Function ◽  
Triangular Lattice ◽  
Incompressible Liquid ◽  
Gaussian Approximation ◽  
Lattice Structure ◽  
Phase Fluctuation ◽  
Probable Distribution ◽  
Crystal Transition ◽  
Laughlin Wave Function ◽  
Most Probable Distribution

We show that, up to a global phase freedom, the most probable distribution of electrons given by the maxima of modulus square of Laughlin wave function (LWF), which is known to be a wave function for an incompressible liquid state of fractional Hall effect, has a triangular lattice structure. We introduce the Gaussian approximation for the modulus square of LWF. We find that the radial distribution function calculated from the Gaussian approximation has a form close to that of LWF at ν = 1, 1/3 and close to a crystal-like behavior when ν becomes smaller. We interprete the underlying physics to be that in the incompressible liquid regime, the "hidden" triangular lattice is smeared away by the quantum phase fluctuation, and as a precursor for liquid-crystal transition when the filling ν decreases towards the crystallization regime, it might manifest itself to be a sort of correlated short-range ordered density fluctuation.

Statistic thermodynamic analysis of fructans – Part 3: Relationship between polymer structure and mixing entropy at equilibrium conditions

2017 ◽  
pp. 151-157
Author(s):  
Roland H.F. Beck
Keyword(s):  
Thermodynamic Analysis ◽  
Polymer Structure ◽  
Degree Of Polymerization ◽  
Average Degree ◽  
Equilibrium Conditions ◽  
Mixing Entropy ◽  
Branching Structures ◽  
Probable Distribution ◽  
Extremum Value ◽  
Most Probable Distribution

The reduced mixing entropy, which is a concentration and unimer independent equivalent to the polymer mixing entropy defined by Flory, for various probabilistic distributed polymer distributions is calculated. The unbranched most probable distribution proves to reach an extremum value at any given number average degree of polymerization, clearly differentiating it from both broader and narrower polymer distributions with branching structures. Entropy driven polymerization reactions thus inevitably produce unbranched polymer structures as discussed for the case of inulin biosynthesis.

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