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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 ...
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 ...
Willard Gibbs, Graphical Methods in the Thermodynamics of Fluids The concept of entropy is described by two principal approaches, the macroscopic perspective of classical thermodynamics, and the microscopic description central to statistical mechanics. The classical approach defines entropy in terms of macroscopically measurable physical properties, such as bulk mass, volume, pressure, and ...
In information theory, the entropy of a random variable quantifies the average level of uncertainty or information associated with the variable's potential states or possible outcomes. This measures the expected amount of information needed to describe the state of the variable, considering the distribution of probabilities across all potential ...
The Clausius theorem is a mathematical representation of the second law of thermodynamics. It was developed by Rudolf Clausius who intended to explain the relationship between the heat flow in a system and the entropy of the system and its surroundings. Clausius developed this in his efforts to explain entropy and define it quantitatively.
The randomness or disorder is maximal, and so is the lack of distinction (or information) of each microstate. Entropy is a thermodynamic property just like pressure, volume, or temperature. Therefore, it connects the microscopic and the macroscopic world view. Boltzmann's principle is regarded as the foundation of statistical mechanics.
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 ...
Interpreted in this way, Boltzmann's formula is the most basic formula for the thermodynamic entropy. Boltzmann's paradigm was an ideal gas of N identical particles, of which Ni are in the i -th microscopic condition (range) of position and momentum. For this case, the probability of each microstate of the system is equal, so it was equivalent ...