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From Citizendium, the Citizens' Compendium
In thermodynamics, an isentropic process is a process of constant entropy. The entropy of a thermodynamic system can change by two causes: (i) by transferral of heat in or out the system, and (ii) by a spontaneous (natural) process inside the system that, by the second law of thermodynamics, is accompanied by an entropy increase.
If a system has adiabatic walls, heat cannot enter or leave the system, and the first cause of possible change of entropy does not occur. A process, taking place without heat entering or exiting, is called an adiabatic process. If a process is quasi-static (also known as reversible), there is no spontaneous increase of entropy, hence, in short, an isentropic process is quasi-static and adiabatic.
In actual practice, quasi-static (reversible) processes do not occur; the concept of reversibility is an idealization, an unachievable limit, but useful for theoretical considerations.