Impact of Interparticle Interaction on Thermodynamics of Nano-Channel Transport of Two Species

Abstract

We present a rigorous mathematical approach of two species channel transport within the framework of stochastic thermodynamics, which explains the impact of interparticle in-channel interactions. Different from mean field approaches, the model explicitly conserves spatial correlations by considering stochastic transitions between the channel's occupation states. The interparticle interactions determine the Brownian ratchet like rectifying forces, which these species exert mutually on each other. Perfect coupling of transport emerges by an attractive empty channel and strong repulsive forces between particles of the same species. Stochastic transitions are then confined to a subspace with circular topology, which makes channel flows of both species become equivalent. For opposing concentration gradients, this makes the species with the stronger gradient the driving, positive entropy producing one, the other is driven and produces negative entropy. A differential interaction with less repulsive forces within particles of one species, but maintenance of this interaction for the other species, adds a bypass path to this circular subspace. On this path a leak flow of the species with less repulsive interparticle interaction emerges, which is directed parallel to its concentration gradient, and, hence, produces positive entropy. Now, appropriate strong opposing concentration gradients may simultaneously parallelize flow of their respective species, which makes each species produce positive entropy. The rectifying potential of the species with the bypass option is diminished, which implies the existence of a gradient of the other species, above which its flow and gradient are always parallel. Conversely flow of the less coupled species may always be turned anti-parallel to its gradient by a sufficient strong opposing gradient of the other one.