Search results
Results from the WOW.Com Content Network
The violet is the mutual information . In information theory, the conditional entropy quantifies the amount of information needed to describe the outcome of a random variable given that the value of another random variable is known. Here, information is measured in shannons, nats, or hartleys. The entropy of conditioned on is written as .
The defining expression for entropy in the theory of information established by Claude E. Shannon in 1948 is of the form: where is the probability of the message taken from the message space M, and b is the base of the logarithm used. 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 ...
Thermodynamics. In thermodynamics, entropy is a numerical quantity that shows that many physical processes can go in only one direction in time. For example, cream and coffee can be mixed together, but cannot be "unmixed"; a piece of wood can be burned, but cannot be "unburned". The word 'entropy' has entered popular usage to refer to a lack of ...
e. Differential entropy (also referred to as continuous entropy) is a concept in information theory that began as an attempt by Claude Shannon to extend the idea of (Shannon) entropy (a measure of average surprisal) of a random variable, to continuous probability distributions. Unfortunately, Shannon did not derive this formula, and rather just ...
Von Neumann entropy. In physics, the von Neumann entropy, named after John von Neumann, is an extension of the concept of Gibbs entropy from classical statistical mechanics to quantum statistical mechanics. For a quantum-mechanical system described by a density matrix ρ, the von Neumann entropy is [1] {\displaystyle S=-\operatorname {tr} (\rho ...
Since an entropy is a state function, the entropy change of the system for an irreversible path is the same as for a reversible path between the same two states. [22] However, the heat transferred to or from the surroundings is different as well as its entropy change. We can calculate the change of entropy only by integrating the above formula.
Definition. A process with a countable index gives rise to the sequence of its joint entropies . If the limit exists, the entropy rate is defined as. := lim → ∞ {\displaystyle H (X):=\lim _ {n\to \infty } {\tfrac {1} {n}}H_ {n}.} Note that given any sequence with and letting , by telescoping one has . The entropy rate thus computes the mean ...
In information theory, the binary entropy function, denoted or , is defined as the entropy of a Bernoulli process (i.i.d. binary variable) with probability of one of two values, and is given by the formula: {\displaystyle \operatorname {H} (X)=-p\log p- (1-p)\log (1-p).} The base of the logarithm corresponds to the choice of units of ...