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Maxwell's demon can (hypothetically) reduce the thermodynamic entropy of a system by using information about the states of individual molecules; but, as Landauer (from 1961) and co-workers [20] have shown, to function the demon himself must increase thermodynamic entropy in the process, by at least the amount of Shannon information he proposes ...
A modified version of MUSIC, denoted as Time-Reversal MUSIC (TR-MUSIC) has been recently applied to computational time-reversal imaging. [11] [12] MUSIC algorithm has also been implemented for fast detection of the DTMF frequencies (Dual-tone multi-frequency signaling) in the form of C library - libmusic [13] (including for MATLAB ...
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. [23] 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.
Cross-entropy can be used to define a loss function in machine learning and optimization. Mao, Mohri, and Zhong (2023) give an extensive analysis of the properties of the family of cross-entropy loss functions in machine learning, including theoretical learning guarantees and extensions to adversarial learning. [3]
Relative entropy relates to "rate function" in the theory of large deviations. [24] [25] Arthur Hobson proved that relative entropy is the only measure of difference between probability distributions that satisfies some desired properties, which are the canonical extension to those appearing in a commonly used characterization of entropy. [26]
More precisely, the source coding theorem states that for any source distribution, the expected code length satisfies [(())] [ (())], where is the number of symbols in a code word, is the coding function, is the number of symbols used to make output codes and is the probability of the source symbol. An entropy coding attempts to ...
the mutual information, and the channel capacity of a noisy channel, including the promise of perfect loss-free communication given by the noisy-channel coding theorem; the practical result of the Shannon–Hartley law for the channel capacity of a Gaussian channel; as well as; the bit—a new way of seeing the most fundamental unit of information.
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.