Search results
Results From The WOW.Com Content Network
One of the main applications of the maximum entropy principle is in discrete and continuous density estimation. [10] [11] Similar to support vector machine estimators, the maximum entropy principle may require the solution to a quadratic programming problem, and thus provide a sparse mixture model as the optimal density estimator. One important ...
The density of the maximum entropy distribution for this class is constant on each of the intervals [a j-1,a j). The uniform distribution on the finite set {x 1,...,x n} (which assigns a probability of 1/n to each of these values) is the maximum entropy distribution among all discrete distributions supported on this set.
The inspiration for adopting the word entropy in information theory came from the close resemblance between Shannon's formula and very similar known formulae from statistical mechanics. In statistical thermodynamics the most general formula for the thermodynamic entropy S of a thermodynamic system is the Gibbs entropy
The von Neumann entropy formula is an extension of the Gibbs entropy formula to the quantum mechanical case. It has been shown [ 1 ] that the Gibbs Entropy is equal to the classical "heat engine" entropy characterized by d S = δ Q T {\displaystyle dS={\frac {\delta Q}{T}}\!} , and the generalized Boltzmann distribution is a sufficient and ...
The relationship between entropy, order, and disorder in the Boltzmann equation is so clear among physicists that according to the views of thermodynamic ecologists Sven Jorgensen and Yuri Svirezhev, "it is obvious that entropy is a measure of order or, most likely, disorder in the system."
Maximum entropy: For given mechanical parameters (fixed V), the grand canonical ensemble average of the log-probability (also called the "entropy") is the maximum possible for any ensemble (i.e. probability distribution P) with the same , , etc. [1]
In physics, maximum entropy thermodynamics (colloquially, MaxEnt thermodynamics) views equilibrium thermodynamics and statistical mechanics as inference processes. More specifically, MaxEnt applies inference techniques rooted in Shannon information theory, Bayesian probability, and the principle of maximum entropy.
The Shannon entropy (in nats) is: = = = and if entropy is measured in units of per nat, then the entropy is given by: = which is the Boltzmann entropy formula, where is the Boltzmann constant, which may be interpreted as the thermodynamic entropy per nat.