The voltage-dependent rate constants of the Hodgkin-Huxley equations for the n, m, and h systems are tested for consistency with the Second Law of Thermodynamics as applied to the kinetic behaviour of independent particles moving in a closed thermodynamic system according to first-order rate laws. No consistency with Boltzmann distribution theory and classical thermodynamics is found for any of the n, m, or h rate constants without the additional proviso that the equivalent valencies of the n, m, and h particles are also voltage-dependent. A model is provided showing how non-linear membrane potential profiles could create an apparent voltage-dependent variation in the equivalent valency of particles experiencing only a fraction of the electric field. There is an unexplained discrepancy between the classical description of the m system and the more recent description of it in association with measurement of gating currents: the classical description requires voltage-dependent valency for thermodynamic consistency whereas the recent description is a thermodynamically formulated one that assumes constant valency independent of voltage for the independent m particles. The formulations presented become void if departures from first order independent behaviour are allowed. © 1980, All rights reserved.
Chapman, J. B. (1980). Consistency between thermodynamics and the kinetics of n, m, and h in the hodgkin-huxley equations. Journal of Theoretical Biology, 85(3), 487–495. https://doi.org/10.1016/0022-5193(80)90322-7