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The first 128 symbols of the Fibonacci sequence has an entropy of approximately 7 bits/symbol, but the sequence can be expressed using a formula [F(n) = F(n−1) + F(n−2) for n = 3, 4, 5, ..., F(1) =1, F(2) = 1] and this formula has a much lower entropy and applies to any length of the Fibonacci sequence.
In information theory, the cross-entropy between two probability distributions and , over the same underlying set of events, measures the average number of bits needed to identify an event drawn from the set when the coding scheme used for the set is optimized for an estimated probability distribution , rather than the true distribution .
Common values of b are 2, Euler's number e, and 10, and the unit of entropy is shannon (or bit) for b = 2, nat for b = e, and hartley for b = 10. [ 1 ] Mathematically H may also be seen as an average information, taken over the message space, because when a certain message occurs with probability p i , the information quantity −log( p i ...
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."
9.5699 × 10 −24 J⋅K −1: Entropy equivalent of one bit of information, equal to k times ln(2) [1] 10 −23: 1.381 × 10 −23 J⋅K −1: Boltzmann constant, entropy equivalent of one nat of information. 10 1: 5.74 J⋅K −1: Standard entropy of 1 mole of graphite [2] 10 33: ≈ 10 35 J⋅K −1: Entropy of the Sun (given as ≈ 10 42 ...
Hirschman [1] explained that entropy—his version of entropy was the negative of Shannon's—is a "measure of the concentration of [a probability distribution] in a set of small measure." Thus a low or large negative Shannon entropy means that a considerable mass of the probability distribution is confined to a set of small measure.
Crocco's theorem is an aerodynamic theorem relating the flow velocity, vorticity, and stagnation pressure (or entropy) of a potential flow. Crocco's theorem gives the relation between the thermodynamics and fluid kinematics. The theorem was first enunciated by Alexander Friedmann for the particular case of a perfect gas and published in 1922: [1]
In quantum field theory, a false vacuum [1] is a hypothetical vacuum state that is locally stable but does not occupy the most stable possible ground state. [2] In this condition it is called metastable. It may last for a very long time in this state, but could eventually decay to the more stable one, an event known as false vacuum decay.