Thermodynamic induction effects exhibited in nonequilibrium systems with variable kinetic coefficients

Abstract

A nonequilibrium thermodynamic theory demonstrating an induction effect of a statistical nature is presented. We have shown that this thermodynamic induction can arise in a class of systems that have variable kinetic coefficients (VKC). In particular if a kinetic coefficient associated with a given thermodynamic variable depends on another thermodynamic variable then we have derived an expression that can predict the extent of the induction. The amount of induction is shown to be proportional to the square of the driving force. The nature of the intervariable coupling for the induction effect has similarities with the Onsager symmetry relations, though there is an important sign difference as well as the magnitudes not being equal. Thermodynamic induction adds nonlinear terms that improve the stability of stationary states, at least within the VKC class of systems. Induction also produces a term in the expression for the rate of entropy production that could be interpreted as self-organization. Many of these results are also obtained using a variational approach, based on maximizing entropy production, in a certain sense. Non-equilibrium quantities analogous to the free energies of equilibrium thermodynamics are introduced.

Thermodynamically induced particle transport: Order-by-induction and entropic trapping at the nano-scale

“…[3]. Given that the total free power must always be negative, the physical meaning for this result is that the magnitude of the total free power is made larger when the fast variables are allowed to relax by moving away from equilibrium values to quasistationary status.…”

“…In this work I follow closely the approach presented in Ref. [3], with the main difference being that in this treatment I assume isothermal conditions, i.e., dT = 0 throughout. This approach involves a coupling of system A to a large heat bath, or reservoir, always held at temperature T .…”

“…Nonlinear effects are manifested in the slowly-varying N pq coefficients which are derived in a procedure very similar to the proof of the principle of thermodynamic induction [3]. The key step in the derivation is to revisit Eq.…”

“…The main result of Ref. [3] is the existence of the previously unknown N ki coefficients (across the diagonal). These induction coefficients change the dynamics of gating variables.…”

“…In Ref. [3] it was suggested that systems that have a bottlenecking or gating property might be good candidates for displaying measurable TI effects. In addition TI predicts the enhancement of transport rates for a bottlenecked process, as a consequence of maximizing entropy production [3].…”