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A 'quasistatic process' is a thermodynamic process that happens infinitely slowly. In practice, such processes can be approximated by performing them "very slowly".
A quasistatic process often ensures that the system will go through a sequence of states that are infinitesimally close to equilibrium, in which case the process is typically reversible. An example of a quasistatic process that is not reversible is the slow heat exchange between two bodies at two finitely different temperatures, where the heat exchange rate is controlled by an approximately adiabatic partition between the two bodies (Sears and Salinger, 1986) — in this case, no matter how slowly the process takes place, the states of the two bodies are never infinitesimally close to equilibrium, since thermal equilibrium requires that the two bodies be at precisely the same temperature.
Some ambiguity exists in the literature concerning the distinction between quasistatic and reversible processes, as these are sometimes taken as synonyms (Lavenda, 1978). The above definition is closer to the intuitive understanding of the word "quasi-" (almost) "static", while remaining technically different from reversible processes.
There is no such thing as an "approximately adiabatic" partition. Every quasi-static adiabatic transition is reversible [cf. H. Buchdahl, The Concepts of Classical Thermodynamics (Cambridge U.P., 1966), p.53]. In addition to being unphysical, the example used to refute this is extremely misleading.

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Bibliography

★ Sears, F.W., Salinger, G.L. (1986), ''Thermodynamics, Kinetic Theory, and Statistical Thermodynamics'', 3rd edition (Addison-Wesley)

★ Lavenda, B.H. (1978), ''Thermodynamics of Irreversible Processes'', Halsted.

See also

★ Reversible process (thermodynamics)