Probability and Entropy of Macroscopic Fluctuations

1966 ◽  
Vol 7 (8) ◽  
pp. 1552-1556
Author(s):  
Robert Zwanzig
Keyword(s):  
Macroscopic Fluctuations

Novel liquid crystal trimers exhibiting a monolayer smectic C phase containing strong macroscopic fluctuations

2007 ◽  
Vol 34 (10) ◽  
pp. 1121-1128 ◽  
Author(s):  
Atsushi Yoshizawa ◽  
Naoki Uehara ◽  
Mariko Kurauchi ◽  
Akihisa Yamaguchi
Keyword(s):  
Liquid Crystal ◽  
Smectic C ◽  
Macroscopic Fluctuations

scholarly journals SPONTANEOUS SCALING EMERGENCE IN GENERIC STOCHASTIC SYSTEMS

1996 ◽  
Vol 07 (05) ◽  
pp. 745-751 ◽  
Author(s):  
SORIN SOLOMON ◽  
MOSHE LEVY
Keyword(s):  
Degrees Of Freedom ◽  
Stochastic Systems ◽  
Evolution Equations ◽  
Power Laws ◽  
Average Value ◽  
Wide Range ◽  
Generic Class ◽  
Parameter Ranges ◽  
Power Law Distributions ◽  
Macroscopic Fluctuations

We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for certain parameter ranges, the new systems fulfill nonlinear time evolution equations similar to the ones encountered in Spontaneous Symmetry Breaking (SSB) dynamics and evolve spontaneously towards "fixed trajectories" indexed by the average value of their degrees of freedom (which corresponds to the SSB order parameter). The "fixed trajectories" dynamics evolves on the edge between explosion and collapse/extinction. The systems present power laws with exponents which in a wide range (α < –2.) are universally determined by the ratio between the minimal and the average values of the degrees of freedom. The time fluctuations are governed by Levy distributions of corresponding power. For exponents α > −2 there is no "thermodynamic limit" and the fluctuations are dominated by a few, largest degrees of freedom which leads to macroscopic fluctuations, chaos, and bursts/intermittency.

Basic phenomena of “macroscopic fluctuations” are repeated on light beams generated by lasers or light-emitting diodes

BIOPHYSICS ◽  
2014 ◽  
Vol 59 (3) ◽  
pp. 492-502
Author(s):  
I. A. Rubinstein ◽  
A. V. Kaminskiy ◽  
A. A. Tolokonnikova ◽  
V. A. Kolombet ◽  
S. E. Shnoll
Keyword(s):  
Light Emitting Diodes ◽  
Light Emitting ◽  
Light Beams ◽  
Macroscopic Fluctuations

scholarly journals Layer histogram patterns in financial time series

2009 ◽  
Vol 6 (3) ◽  
pp. 137-146
Author(s):  
Verena Helen Van Zyl-Bulitta ◽  
R. Otte ◽  
JH Van Rooyen
Keyword(s):  
Time Series ◽  
Exchange Rate ◽  
Financial Risk ◽  
Pattern Analysis ◽  
Financial Time Series ◽  
Data Set ◽  
Frequency Distributions ◽  
Analysis Techniques ◽  
Financial Time ◽  
Macroscopic Fluctuations

This study aims to investigate whether the phenomena found by Shnoll et al. when applying histogram pattern analysis techniques to stochastic processes from chemistry and physics are also present in financial time series, particularly exchange rate and index data. The phenomena are related to fine structure of non-smoothed frequency distributions drawn from statistically insufficient samples of changes and their patterns in time. Shnoll et al. use the notion of macroscopic fluctuations (MF) to explain the behavior of sequences of histograms. Histogram patterns in time adhere to several laws that could not be detected when using time series analysis methods. In this study special emphasis is placed on the histogram pattern analysis of high frequency exchange rate data set. Following previous studies of the Shnoll phenomena from other fields, different steps of the histogram sequence analysis are carried out to determine whether the findings of Shnoll et al. could also be applied to financial market data. The findings presented here widen the understanding of time varying volatility and can aid in financial risk measurement and management. Outcomes of the study include an investigation of time series characteristics, more specifically the formation of discrete states.

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