Functional Integrals Representing Distribution Functions in Statistical Mechanics

1969 ◽  
Vol 10 (4) ◽  
pp. 675-682 ◽  
Author(s):  
Clas Blomberg
Keyword(s):  
Statistical Mechanics ◽  
Distribution Functions ◽  
Functional Integrals

Statistical Mechanics and Information Theory for Complex Systems

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Information Theory ◽  
Statistical Mechanics ◽  
Complex Systems ◽  
Maximum Entropy Principle ◽  
Distribution Functions ◽  
Complex Processes ◽  
Entropy Principle ◽  
Path Dependent ◽  
Statistical Systems ◽  
Dependent Processes

Most complex systems are statistical systems. Statsitical mechanics and information theory usually do not apply to complex systems because the latter break the assumptions of ergodicity, independence, and multinomial statistics. We show that it is possible to generalize the frameworks of statistical mechanics and information theory in a meaningful way, such that they become useful for understanding the statistics of complex systems.We clarify that the notion of entropy for complex systems is strongly dependent on the context where it is used, and differs if it is used as an extensive quantity, a measure of information, or as a tool for statistical inference. We show this explicitly for simple path-dependent complex processes such as Polya urn processes, and sample space reducing processes.We also show it is possible to generalize the maximum entropy principle to path-dependent processes and how this can be used to compute timedependent distribution functions of history dependent processes.

IMPLICATIONS OF INTERPOLATIVE QUANTUM STATISTICS — A REVIEW

1995 ◽  
Vol 09 (03n04) ◽  
pp. 135-143 ◽  
Author(s):  
R. RAMANATHAN
Keyword(s):  
Distribution Function ◽  
Statistical Mechanics ◽  
Distribution Functions ◽  
Quantum Statistics ◽  
Physical Processes ◽  
Positivity Condition ◽  
Statistical Interaction

A review of the interpolative quantum statistics is presented. It is shown, by imposing a positivity condition on the distribution function, that this statistics subsumes Gentile's intermediate statistics and is far richer than Gentile's statistics, apart from being a genuine quantum statistics. It is also capable of accounting for the possible very small violations of statistics in physical processes. It is finally pointed out that this statistics offers an elegant and useful parametrization of Haldane's 'statistical interaction', while retaining all the interesting features of the latter. Some of the statistical mechanics that these distribution functions lead to are also examined.

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