Role of the nature of noise in the thermal conductance of mechanical systems

Focusing on a paradigmatic small system consisting of two coupled damped oscillators, we survey the role of the Lévy-Itô nature of the noise in the thermal conductance. For white noises, we prove that the Lévy-Itô composition (Lebesgue measure) of the noise is irrelevant for the thermal conductance of a nonequilibrium linearly coupled chain, which signals the independence of mechanical and thermodynamical properties. In contrast, for the nonlinearly coupled case, the two types of properties mix and the explicit definition of the noise plays a central role.

Figure 1

Average exchange flux $\langle j_{12}\rangle$ of a two-massive-particle system for different combinations of paradigmatic types of noise with $T_1=10$, $T_2=121/10$, $m=10$, $\gamma =k=1$, $k_1=1/5$, $k_3=0$, and $\lambda =10$ for Poissonian particles. After the transient, $\kappa$ agrees with the theoretical value, $\kappa =21/800=0.02625$, with the fitting curves lying within the line thickness. The averages have been obtained by averaging over $850\times (5\times {10}^5)$ points. The discretization used is $\delta t={10}^{-5}$ with snapshots at every $\Delta t={10}^{-3}$.

Figure 2

Comparison between numerically obtained values (symbols) and the first-order approximation of thermal conductance from Eqs. (8, 9, 10) for different temperature pairs, namely, $A=\{10,\frac{169}{10}\}$, $B=\{10,\frac{225}{10}\}$, and $C=\{10,\frac{289}{10}\}$ with $m=10$, $\gamma =k=1$, $k_1=1/5$, and $\lambda =1$ for Poissonian particles.