In this paper we examine the connection between emittance growth and entropy growth in linear accelerators. We divide emittance growth into two classes: reversible and irreversible, depending on the corresponding entropy change. We propose the general hypothesis that if (Delta) E > 0 and (Delta) S equals 0, then the emittance growth may be reversible. We also propose that if (Delta) E > 0 and (Delta) S > 0 then the emittance growth is irreversible. We outline how the concept may be applied to particular cases of relevance e.g. emittance growth and recovery in electron photoinjectors, and wakefield induced emittance growth, where correlations are introduced in the transverse phase space.