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The principle of maximum entropy states that the probability distribution which best represents the current state of knowledge about a system is the one with largest entropy, in the context of precisely stated prior data (such as a proposition that expresses testable information).
In physics, maximum entropy thermodynamics (colloquially, MaxEnt thermodynamics) views equilibrium thermodynamics and statistical mechanics as inference processes. More specifically, MaxEnt applies inference techniques rooted in Shannon information theory, Bayesian probability, and the principle of maximum entropy.
The density of the maximum entropy distribution for this class is constant on each of the intervals [a j-1,a j). The uniform distribution on the finite set {x 1,...,x n} (which assigns a probability of 1/n to each of these values) is the maximum entropy distribution among all discrete distributions supported on this set.
Thus, if entropy is associated with disorder and if the entropy of the universe is headed towards maximal entropy, then many are often puzzled as to the nature of the "ordering" process and operation of evolution in relation to Clausius' most famous version of the second law, which states that the universe is headed towards maximal "disorder".
The heat death of the universe (also known as the Big Chill or Big Freeze) [1] [2] is a hypothesis on the ultimate fate of the universe, which suggests the universe will evolve to a state of no thermodynamic free energy, and will therefore be unable to sustain processes that increase entropy.
Jaynes around 1982. Edwin Thompson Jaynes (July 5, 1922 – April 30, [1] 1998) was the Wayman Crow Distinguished Professor of Physics at Washington University in St. Louis.He wrote extensively on statistical mechanics and on foundations of probability and statistical inference, initiating in 1957 the maximum entropy interpretation of thermodynamics [2] [3] as being a particular application of ...
The concept of information entropy was introduced by Claude Shannon in his 1948 paper "A Mathematical Theory of Communication", [2] [3] and is also referred to as Shannon entropy. Shannon's theory defines a data communication system composed of three elements: a source of data, a communication channel , and a receiver.
(These perspectives are explored further in the article Maximum entropy thermodynamics.) The Shannon entropy in information theory is sometimes expressed in units of bits per symbol. 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.