Entropy is a measure of the energy of a system that is unavailable for doing useful work. In statistical thermodynamics, entropy (usual symbol S) is a measure of the number of microscopic configurations Ω that correspond to a thermodynamic system in a state specified by certain macroscopic variables. Specifically, assuming that each of the microscopic configurations is equally probable, the entropy of the system is the natural logarithm of that number of configurations, multiplied by the Boltzmann constant kB (which provides consistency with the original thermodynamic concept of entropy discussed below, and gives entropy the dimension of energy divided by temperature). Formally,

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• Entropy is a measure of the energy of a system that is unavailable for doing useful work. In statistical thermodynamics, entropy (usual symbol S) is a measure of the number of microscopic configurations Ω that correspond to a thermodynamic system in a state specified by certain macroscopic variables. Specifically, assuming that each of the microscopic configurations is equally probable, the entropy of the system is the natural logarithm of that number of configurations, multiplied by the Boltzmann constant kB (which provides consistency with the original thermodynamic concept of entropy discussed below, and gives entropy the dimension of energy divided by temperature). Formally, For example, gas in a container with known volume, pressure, and temperature could have an enormous number of possible configurations of the individual gas molecules, and which configuration the gas is actually in may be regarded as random. Hence, entropy can be understood as a measure of molecular disorder within a macroscopic system. The second law of thermodynamics states that an isolated system's entropy never decreases. Such systems spontaneously evolve towards thermodynamic equilibrium, the state with maximum entropy. Non-isolated systems may lose entropy, provided their environment's entropy increases by at least that decrement. Since entropy is a state function, the change in entropy of a system is determined by its initial and final states. This applies whether the process is reversible or irreversible. However, irreversible processes increase the combined entropy of the system and its environment. The change in entropy (ΔS) of a system was originally defined for a thermodynamically reversible process as , where T is the absolute temperature of the system, dividing an incremental reversible transfer of heat into that system (δQrev). (If heat is transferred out the sign would be reversed giving a decrease in entropy of the system.) The above definition is sometimes called the macroscopic definition of entropy because it can be used without regard to any microscopic description of the contents of a system. The concept of entropy has been found to be generally useful and has several other formulations. Entropy was discovered when it was noticed to be a quantity that behaves as a function of state, as a consequence of the second law of thermodynamics. Entropy is an extensive property. It has the dimension of energy divided by temperature, which has a unit of joules per kelvin (J K−1) in the International System of Units (or kg m2 s−2 K−1 in terms of base units). But the entropy of a pure substance is usually given as an intensive property—either entropy per unit mass (SI unit: J K−1 kg−1) or entropy per unit amount of substance (SI unit: J K−1 mol−1). The absolute entropy (S rather than ΔS) was defined later, using either statistical mechanics or the third law of thermodynamics, an otherwise arbitrary additive constant is fixed such that the entropy at absolute zero is zero. In statistical mechanics this reflects that the ground state of a system is generally non-degenerate and only one microscopic configuration corresponds to it. In the modern microscopic interpretation of entropy in statistical mechanics, entropy is the amount of additional information needed to specify the exact physical state of a system, given its thermodynamic specification. Understanding the role of thermodynamic entropy in various processes requires an understanding of how and why that information changes as the system evolves from its initial to its final condition. It is often said that entropy is an expression of the disorder, or randomness of a system, or of our lack of information about it. The second law is now often seen as an expression of the fundamental postulate of statistical mechanics through the modern definition of entropy. (en)
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• Any method involving the notion of entropy, the very existence of which depends on the second law of thermodynamics, will doubtless seem to many far-fetched, and may repel beginners as obscure and difficult of comprehension.
• I thought of calling it "information", but the word was overly used, so I decided to call it "uncertainty". [...] Von Neumann told me, "You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, nobody knows what entropy really is, so in a debate you will always have the advantage."
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• Willard Gibbs, Graphical Methods in the Thermodynamics of Fluids
• Conversation between Claude Shannon and John von Neumann regarding what name to give to the attenuation in phone-line signals
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• Entropy is a measure of the energy of a system that is unavailable for doing useful work. In statistical thermodynamics, entropy (usual symbol S) is a measure of the number of microscopic configurations Ω that correspond to a thermodynamic system in a state specified by certain macroscopic variables. Specifically, assuming that each of the microscopic configurations is equally probable, the entropy of the system is the natural logarithm of that number of configurations, multiplied by the Boltzmann constant kB (which provides consistency with the original thermodynamic concept of entropy discussed below, and gives entropy the dimension of energy divided by temperature). Formally, (en)
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• Entropy (en)
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