Negative Differential Heat Conductivity in a Harmonic Chain Coupled to a Particle Reservoir

Abstract

When coupling thermal baths at different temperatures, negative differential thermal conductivity is typically attributed to nonlinear interactions in the connecting medium. In this work, we demonstrate that such an effect can arise purely from the nature of the thermal baths and their coupling with the medium. Specifically, we construct a bath composed of overdamped thermal particles, which is coupled to one end of a harmonic chain, while the other end is connected to a standard Langevin heat bath. By analyzing the steady-state heat current, we observe significant negative differential thermal conductivity. In particular, as the temperature difference between the two baths diverges, the steady-state heat current through the chain vanishes. The effect is thermokinetic: we compute the effective dissipative coefficient and we find that it scales inversely with the square of the temperature of the particle bath in the high-temperature limit, resulting in an asymptotic decoupling between the bath and the chain. Our results highlight that nonequilibrium transport properties can be strongly influenced by the structure of the environment and its coupling to the system, even in otherwise linear systems.

Figures (4)

• Figure 1: Schematic of the setup with the particle bath on the left, and the Langevin bath on the right. The membrane is modeled by a succession of springs with displacement $q_{1\ldots N}$.
• Figure 2: (a) Mean force exerted by the particle bath at fixed $q$ and temperature $T_L$, with $\varepsilon=10^{-3}$. (b) Plot of the effective friction experienced by a single oscillator in the embedded bath with the bath temperature. The points denote the $\gamma_\text{eff}$ extracted from the simulations using Eq. \ref{['eq:veldecay']}, while the dashed lines denote the prediction Eq. \ref{['eq:gammaGK']} for $m=1$, $k=1$, $N_b=40$, $\zeta=0.1$, $\lambda=1$, $p=2$, and $L=25$.
• Figure 3: Simulation result for the mean current through the chain for several values of the friction coefficient of the bath particles $\zeta$. Lower friction implies better time-scale separation. (a) linear scale, with comparison to theoretical prediction (solid line). (b) log-log plot which displays $\langle J\rangle \propto T_L^{-1}$ behavior at high $T_L$.
• Figure 4: Simulation results of the mean current through the chain, now with $T_L\neq T_R$ to disentangle $T_{L}$ and $\Delta=\abs{T_{R}-T_{L}}$. (a) Mean current for the chain for various spring constants, and $T_R=10$. Nonmonotonic behavior is also observed when $T_L<T_R$, (b) Juxtaposition of the respective currents when $T_L$ and $T_R$ are kept constant. Varying $T_L$ produces nonlinear dependency of the current on the temperature; varying $T_R$ reproduces the typical linear behavior.