Cross-Influence of Thermodynamic Driving Forces in Confined Environment

The second law of thermodynamics dictates that under a certain condition, the cross-influences of thermodynamic driving forces (tdf) must be balanced. For a galvanic cell, it is equivalent to the well-known Nernst equation; for a double-layer supercapacitor, it is consistent with the classic Gouy-Chapman model. In our recent experiment on confined large pivalate ions in carbon nanopores, however, it was measured that the cross-influences of the electromotive force and the chemical potential were different from each other by an order of magnitude. We attribute this remarkable phenomenon to the confinement effect of the electrode inner surfaces, which forbids the formation of diffuse layer. We argue that in general, in a low-dimensional environment, in the large dimension(s), the laws of classic statistical physics can be applied; but in the small dimension(s) wherein two tdf interact, the governing equations can be distinct. With this unique mechanism, the second law of thermodynamics may break down, in a dissimilar manner to “Maxwell’s demon”. The concept of unbalanced cross-influence of tdf is further examined through a theoretical analysis on a model system comprising of randomly moving elastic particles restricted in a two-dimensional transition zone in a gravitational field.