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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.
The information gain in decision trees (,), which is equal to the difference between the entropy of and the conditional entropy of given , quantifies the expected information, or the reduction in entropy, from additionally knowing the value of an attribute . The information gain is used to identify which attributes of the dataset provide the ...
To do this, one must acknowledge the difference between the measured entropy of a system—which depends only on its macrostate (its volume, temperature etc.)—and its information entropy, [6] which is the amount of information (number of computer bits) needed to describe the exact microstate of the system. The measured entropy is independent ...
An information diagram is a type of Venn diagram used in information theory to illustrate relationships among Shannon's basic measures of information: entropy, joint entropy, conditional entropy and mutual information. [1] [2] Information
Redundancy of compressed data refers to the difference between the expected compressed data length of messages () (or expected data rate () /) and the entropy (or entropy rate ). (Here we assume the data is ergodic and stationary , e.g., a memoryless source.)
The mutual information is used to learn the structure of Bayesian networks/dynamic Bayesian networks, which is thought to explain the causal relationship between random variables, as exemplified by the GlobalMIT toolkit: [37] learning the globally optimal dynamic Bayesian network with the Mutual Information Test criterion.
To find the entropy difference between any two states of the system, the integral must be evaluated for some reversible path between the initial and final states. [21] 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]
Ludwig Boltzmann defined entropy as a measure of the number of possible microscopic states (microstates) of a system in thermodynamic equilibrium, consistent with its macroscopic thermodynamic properties, which constitute the macrostate of the system. A useful illustration is the example of a sample of gas contained in a container.