Inverse Currents in Hamiltonian Coupled Transport

The occurrence of an inverse current, where the sign of the induced current is opposite to the applied force, is a highly counterintuitive phenomenon. We show that inverse currents in coupled transport (ICC) of energy and particle can occur in a one-dimensional interacting Hamiltonian system when its equilibrium state is perturbed by coupled thermodynamic forces. This seemingly paradoxical result is possible due to the self-organization occurring in the system in response to the applied forces.

Figure 1

Schematic drawing of the 1D, two masses, interacting gas model. It consists of a diatomic gas of particles which, for visualization purposes, we represent by bullets and rods, respectively. The system is coupled to two reservoirs at its two ends, with which the rods exchange energy while the bullets exchange both energy and particles.

Figure 2

The particle current $J_{\rho }$ (a) and the energy current $J_u$ (b) as a function of the thermodynamic force ${\mathcal{F}}_u$ with ${\mathcal{F}}_{\rho }=0$. The negative particle current $J_{\rho }$ indicates ICC. The system size is $L=20$. (c) and (d) are the same as (a) and (b), respectively, but for the currents as a function of the thermodynamic force ${\mathcal{F}}_{\rho }$ (with ${\mathcal{F}}_u=0$). Here ICC is indicated by the negative energy current $J_u$.

Figure 3

The particle current $J_{\rho }$ (a) and the energy current $J_u$ (b) as a function of the thermodynamic forces ${\mathcal{F}}_u$ and ${\mathcal{F}}_{\rho }$. ICC occurs in $J_{\rho }$ when the thermodynamic forces fall in the area above the white dashed curve in (a) while it occurs in $J_u$ when the thermodynamic forces fall in the area below the white dashed curve in (b). The system size is $L=20$.

Figure 4

The dependence on the interaction potential barrier $h$ of (a) the particle current $J_{\rho }$ and (b) the Onsager cross coefficient ${\mathcal{L}}_{\rho u}$. The thermodynamic forces are ${\mathcal{F}}_{\rho }=0$ and ${\mathcal{F}}_u=0.1$, respectively, and the system size is $L=160$.

Figure 5

(a) The particle current $J_{\rho }$ as a function of the thermodynamic force ${\mathcal{F}}_u$ with ${\mathcal{F}}_{\rho }=0$. The system size is $L=1280$. The inset shows ${\tilde{\mathcal{L}}}_{\rho u}\equiv J_{\rho }L/{\mathcal{F}}_u$. (b) The average mass of all particles passing a given point $x$ along the system. The five curves correspond to the middle five points shown in panel (a).