{'fraction_non_alphanumeric': 0.01651376146788991, 'fraction_numerical': 0.0, 'mean_word_length': 5.380116959064328, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Reversible adiabatic and isentropic changes in quantum systems

In traditional thermodynamics it is assumed that isentropic, reversible, adiabatic processes can be summoned up on demand and straightforwardly accomplished. By contrast, taking entropy as the maximised uncertainty of a final equilibrium state of a quantised system, it is not obvious that an associated process can always be found that is both rigorously isentropic and reversibly adiabatic. In fact, we find that linear relations between generalized forces Xj (such as pressures Pj) and energies Ej are necessary and sufficient conditions for a reversible quasi-static and adiabatic change to be truly isentropic. However, such relationships only hold for a few especially simple systems, such as the perfect gas and the idealised paramagnet. They do not generally hold to all orders for more complicated systems. By considering the associated entropy increases up to second order in small changes of the conjugate displacements (such as the volume Vj) we argue that the consequences are nevertheless in practice negligible.