Exact time-averaged thermal conductance for small systems: Comparison between direct calculation and Green-Kubo formalism

Abstract

In this paper, we study exactly the thermal conductance for a low dimensional system represented by two coupled massive Brownian particles, both directly and via a Green-Kubo expression. Both approaches give exactly the same result. We also obtain exactly the steady-state probability distribution for that system by means of time averaging.

Exact cumulant Kramers–Moyal-like expansion

“…Our approach is generic in principle, but we chose to illustrate the procedures by the use of linear Markovian mechanical models for Gaussian, and non-Gaussian noise. We use a formalism based on the Laplace transform that has been used to obtain exact results for Langevin equations in the context of Markovian and non-Markovian noise [15,16], thermal conductance for linear [17] and non-linear systems [18], fluctuation relations for the work [19], and non Gaussian noises [20,21,18,22]. This method is equivalent to taking into account all noise cumulants, which can be of finite or infinite in number.…”

Exact nonequilibrium work generating function for a small classical system

“…We can integrate this system exactly by techniques similar to the ones used previously [31,32,36], where the integration paths are all described therein. However, at present, we will use a direct solution technique which is different, and simpler than that in references [31,32,36].…”

“…However, at present, we will use a direct solution technique which is different, and simpler than that in references [31,32,36].…”

“…We calculated exactly the model dynamics, in the spirit of other models previously used by the authors [31,32], and we analyzed the behavior of external work fluctuations that are in contact with thermal bath. The thermal bath is represented by a noise term in a Langevin equation (LE) [33].…”

Particle-shape-, temperature-, and concentration-dependent thermal conductivity and viscosity of nanofluids

“…A variety of modeling techniques have been developed for calculating the thermophysical properties over the years [19][20][21]. Among them, molecular dynamics (MD) simulation can provide detailed atomic-level information and has been widely employed in many numerical studies on the thermophysical properties of fluids [22][23][24].…”