Shannon entropy Definition and 14 Threads

Unfortunately, I have problems with the following task For task 1, I proceeded as follows. Since the four bases have the same probability, this is ##P=\frac{1}{4}## I then simply used this probability in the formula for the Shannon entropy...

Hello everyone. I am working with mathematica, where I have developed a two-dimensional shannon interplation, just as can be seen in the slides 15 to 18 of this presentation. The code is as follows: savedX = Table[XposX = mat[[All, 1]]; YposX = mat[[All, 2]]; windXVal = mat[[All, i]]...

I have used the Lagrange multiplier way of answering. So I have set up the equation with the constraint that ## \sum_{x}^{} p(x) = 1## So I have: ##L(x,\lambda) = - \sum_{x}^{} p(x)log_{2}p(x) - \lambda(\sum_{x}^{} p(x) - 1) = 0## I am now supposed to take the partial derivatives with respect...

Definition 1 The von Neumann entropy of a density matrix is given by $$S(\rho) := - Tr[\rho ln \rho] = H[\lambda (\rho)] $$ where ##H[\lambda (\rho)]## is the Shannon entropy of the set of probabilities ##\lambda (\rho)## (which are eigenvalues of the density operator ##\rho##). Definition 2 If...

I'm wondering about the exact usage of the term entropy in programming vs. entropy in science.

Consider three identical boxes of volume V. the first two boxes will contain particles of two different species 'N' and 'n'. The first box contains 'N' identical non interacting particles in a volume V. The second box contains 'n' non interacting particles. The third box is the result of mixing...

Hi I'm having some trouble understanding Shannon entropy and its relation to "computer" bits (zeros and ones). Shannon entropy of a random variable is (assume b=2 so that we work in bits) and everywhere I've read says it is "the number of bits on the average required to describe the random...

If you have multiple possible states of a system then the Shannon entropy depends upon whether the outcomes have equal probability. A predictable outcome isn't very informative after all. But this seems to rely on the predictive ability of the system making the observation/measurement. This...

Homework Statement A particular logic gate takes two binary inputs A and B and has two binary outputs A' and B'. I won't reproduce the truth table. Suffice to say every combination of A and B is given. The output is produced by A' = \text{NOT} \ A and B' = \text{NOT} \ B . The input has...

Hello Community, I have a question that I'm struggling to get clarification on and I would greatly appreciate your thoughts. Big bang theories describe an extremely low thermodynamic entropy (S) state of origin (very ordered). Question: Is the big bang considered to be a high or low shannon...

To encode a symbol in binary form, I need 3 bits ,and I have 6 symbols. So I need 6*3=18 bits to encode "We are" into binary form. As shown in http://www.shannonentropy.netmark.pl/calculate My question: 3 bits to encode one then I have to use 16 bits, _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _. How to...

Shannon entropy of "QXZ" Hello everyone. I am trying to determine the Shannon entropy of the string of letters QXZ, taking into consideration those letters' frequency in English. I am using the formula: [SIZE="4"]H(P) = –Ʃ pilog2pi What's puzzling me is that I am expecting to calculate a...

Is it ever useful to find the Shannon entropy or information content of a wave function? Thanks.

consider a pack of 52 cards in a bridge game. a player try to convey 13 cards by nods of head or shake of heads to his partner. find the shannon entropy