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H is a forerunner of Shannon's information entropy. Claude Shannon denoted his measure of information entropy H after the H-theorem. [17] The article on Shannon's information entropy contains an explanation of the discrete counterpart of the quantity H, known as the information
The physical entropy may be on a "per quantity" basis (h) which is called "intensive" entropy instead of the usual total entropy which is called "extensive" entropy. The "shannons" of a message (Η) are its total "extensive" information entropy and is h times the number of bits in the message.
Entropy is a scientific concept that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory.
The energy and entropy of unpolarized blackbody thermal radiation, is calculated using the spectral energy and entropy radiance expressions derived by Max Planck [63] using equilibrium statistical mechanics, = (), = ((+) (+) ()) where c is the speed of light, k is the Boltzmann constant, h is the Planck constant, ν is frequency ...
The entropy is thus a measure of the uncertainty about exactly which quantum state the system is in, given that we know its energy to be in some interval of size . Deriving the fundamental thermodynamic relation from first principles thus amounts to proving that the above definition of entropy implies that for reversible processes we have:
It is in this sense that entropy is a measure of the energy in a system that cannot be used to do work. An irreversible process degrades the performance of a thermodynamic system, designed to do work or produce cooling, and results in entropy production. The entropy generation during a reversible process is zero. Thus entropy production is a ...
Entropy has been historically, e.g. by Clausius and Helmholtz, associated with disorder. However, in common speech, order is used to describe organization, structural regularity, or form, like that found in a crystal compared with a gas. This commonplace notion of order is described quantitatively by Landau theory.
where T = temperature, S = entropy, p = pressure, V = volume. N i is the number of particles of type i in the system and μ i is the chemical potential for an i-type particle.The set of all N i are also included as natural variables but may be ignored when no chemical reactions are occurring which cause them to change.