Gibbs' paradox and non-uniform convergence

Synthese 81 (3):283 - 312 (1989)
It is only when mixing two or more pure substances along a reversible path that the entropy of the mixing can be made physically manifest. It is not, in this case, a mere mathematical artifact. This mixing requires a process of successive stages. In any finite number of stages, the external manifestation of the entropy change, as a definite and measurable quantity of heat, isa fully continuous function of the relevant variables. It is only at an infinite and unattainable limit thata non-uniform convergence occurs. And this occurs when considered in terms of the number of stages together with a distinguishability parameter appropriate to the particular device which is used to achieve reversibility. These considerations, which are of technological interest to chemical engineers, resolve a paradox derived in chemical theory called Gibbs'' Paradox.
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DOI 10.1007/BF00869318
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V. Mosini (1995). Fundamentalism, Antifundamentalism, and Gibbs' Paradox. Studies in History and Philosophy of Science Part B 26 (2):151-162.

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