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Entropy (classical thermodynamics)
Entropy is a property of thermodynamical systems invented by Rudolf Clausius who named it from the Greek word ''τρoπή'', "transformation". Later Ludwig Boltzmann described the entropy as a measure of the number of possible microscopic configurations ''Ω'' of the individual atoms and molecules of the system (microstates) which comply with the macroscopic state (macrostate) of the system. Boltzmann then went on to show that ''k''ln''Ω'' was equal to the thermodynamic entropy. The factor ''k'' has since been known as Boltzmann's constant.
==Introduction==
In a thermodynamic system, in a horizontal plane, pressure differences, density differences, and temperature differences all tend to equalize over time. For example, consider a room containing a glass of melting ice as one system. The difference in temperature between the warm room and the cold glass of ice and water is equalized as heat from the room is transferred to the cooler ice and water mixture. Over time the temperature of the glass and its contents and the temperature of the room achieve balance. The entropy of the room has decreased. However, the entropy of the glass of ice and water has increased more than the entropy of the room has decreased. In an isolated system, such as the room and ice water taken together, the dispersal of energy from warmer to cooler regions always results in a net increase in entropy. Thus, when the system of the room and ice water system has reached temperature equilibrium, the entropy change from the initial state is at its maximum. The entropy of the thermodynamic system is a measure of how far the equalization has progressed.
There are many irreversible processes that result in an increase of the entropy. See: Entropy production. One of them is mixing of two or more different substances. The mixing is accompanied by the entropy of mixing. If the substances originally are at the same temperature and pressure, there will be no net exchange of heat or work in many important cases, such as mixing of ideal gases. The entropy increase will be entirely due to the mixing of the different substances.〔See, e.g., (Notes for a “Conversation About Entropy” ) for a brief discussion of ''both'' thermodynamic and "configurational" ("positional") entropy in chemistry.〕
From a ''macroscopic perspective'', in classical thermodynamics, the entropy is a state function of a thermodynamic system: that is, a property depending only on the current state of the system, independent of how that state came to be achieved. Entropy is a key ingredient of the Second law of thermodynamics, which has important consequences e.g. for the performance of heat engines, refrigerators, and heat pumps.
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