Statistical Thermodynamics of Mixtures of Rodlike Particles. 3. The Most Probable Distribution

1978 ◽  
Vol 11 (6) ◽  
pp. 1126-1133 ◽  
Author(s):  
Paul J. Flory ◽  
Randall S. Frost
Keyword(s):  
Statistical Thermodynamics ◽  
Probable Distribution ◽  
Thermodynamics Of Mixtures ◽  
Rodlike Particles ◽  
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.

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