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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.
Boltzmann's equation—carved on his gravestone. [1]In statistical mechanics, Boltzmann's equation (also known as the Boltzmann–Planck equation) is a probability equation relating the entropy, also written as , of an ideal gas to the multiplicity (commonly denoted as or ), the number of real microstates corresponding to the gas's macrostate:
The von Neumann entropy formula is an extension of the Gibbs entropy formula to the quantum mechanical case. It has been shown [ 1 ] that the Gibbs Entropy is equal to the classical "heat engine" entropy characterized by d S = δ Q T {\displaystyle dS={\frac {\delta Q}{T}}\!} , and the generalized Boltzmann distribution is a sufficient and ...
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 ...
Generally, information entropy is the average amount of information conveyed by an event, when considering all possible outcomes. 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.
Chemical potential. Particle number. In classical thermodynamics, entropy (from Greek τρoπή (tropḗ) 'transformation') is a property of a thermodynamic system that expresses the direction or outcome of spontaneous changes in the system. The term was introduced by Rudolf Clausius in the mid-19th century to explain the relationship of the ...
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 ...
The relationship between entropy, order, and disorder in the Boltzmann equation is so clear among physicists that according to the views of thermodynamic ecologists Sven Jorgensen and Yuri Svirezhev, "it is obvious that entropy is a measure of order or, most likely, disorder in the system."