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The fact that this smoothing did not remove any information-carrying signal from the microstate sequence and that furthermore the original microstate sequences and the regressors show the same relative behavior at temporal scales about two orders of magnitude apart suggests that the time courses of the EEG microstates are scale invariant."
In statistical mechanics, a microstate is a specific configuration of a system that describes the precise positions and momenta of all the individual particles or components that make up the system. Each microstate has a certain probability of occurring during the course of the system's thermal fluctuations .
which is recognized as the probability of some microstate given a prescribed macrostate using the Gibbs rotational ensemble. [ 1 ] [ 3 ] [ 2 ] The term E i − ω → ⋅ J → i {\displaystyle E_{i}-{\vec {\omega }}\cdot {\vec {J}}_{i}} can be recognized as the effective Hamiltonian H {\displaystyle {\mathcal {H}}} for the system, which then ...
In probability theory and statistics, the F-distribution or F-ratio, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor), is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA) and other F-tests.
Boltzmann's equation—carved on his gravestone. [1]In statistical mechanics, Boltzmann's equation (also known as the Boltzmann–Planck equation) is a probability equation relating the entropy, also written as , of an ideal gas to the multiplicity (commonly denoted as or ), the number of real microstates corresponding to the gas's macrostate:
In simple terms, the microcanonical ensemble is defined by assigning an equal probability to every microstate whose energy falls within a range centered at E. All other microstates are given a probability of zero. Since the probabilities must add up to 1, the probability P is the inverse of the number of microstates W within the range of energy,
A microstate of the system is a description of the positions and momenta of all its particles. The large number of particles of the gas provides an infinite number of possible microstates for the sample, but collectively they exhibit a well-defined average of configuration, which is exhibited as the macrostate of the system, to which each ...
Despite the foregoing, there is a difference between the two quantities. The information entropy Η can be calculated for any probability distribution (if the "message" is taken to be that the event i which had probability p i occurred, out of the space of the events possible), while the thermodynamic entropy S refers to thermodynamic probabilities p i specifically.