Validates Onsager reciprocity in charged membranes, highlighting modeling implications.
Apparent violations of Onsager reciprocity continue to be reported in models of transport through charged membranes and concentrated electrolytes, with asymmetric cross-coefficients frequently interpreted as evidence of broken microscopic reversibility. We develop a thermodynamic framework that clarifies when such asymmetries represent genuine non-reciprocal behaviour and when they are artefacts of modelling and data reduction. Using a charged-membrane cell model as a case study, we formulate entropy production in terms of conjugate flux–force pairs, construct the full symmetric Onsager matrix, and then analyse how variable reduction, spatial averaging, and concentration-dependent parameterisation affect the resulting reduced kinetic coefficients. Numerical reconstructions of published cross-coefficients, together with controlled examples based on explicitly symmetric Onsager matrices, show that nonlinear, concentration-dependent reductions can generate pronounced and systematically ordered separations between effective coefficients, even when the underlying phenomenological matrix remains exactly symmetric. We further distinguish equilibrium linear-response coefficients from finite-amplitude, steady-state effective parameters and discuss the impact of temporal memory effects in concentrated electrolytes. Taken together, these results demonstrate that the reported asymmetries in charged-membrane models do not constitute a violation of Onsager reciprocity and provide practical criteria for testing reciprocity claims in complex coupled transport systems.
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Elijah Lator (2026) studied this question.
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