Nonequilibrium Statistical Mechanics of the Heat Bath for Two Brownian Particles

We propose a new look at the heat bath for two Brownian particles, in which the heat bath as a “system” is both perturbed and sensed by the Brownian particles. Nonlocal thermal fluctuations give rise to bath-mediated static forces between the particles. Based on the general sum rule of the linear response theory, we derive an explicit relation linking these forces to the friction kernel describing the particles’ dynamics. The relation is analytically confirmed in the case of two solvable models and could be experimentally challenged. Our results point out that the inclusion of the environment as a part of the whole system is important for micron- or nanoscale physics.

Figure 1

Two Brownian particles (filled disks, $J=1$ and $J=2$) are trapped by an external potential, such as through optical traps (vertical cones), and interact through both the direct and the heat-bath-mediated interactions.

Figure 2

(a) Hamiltonian model of two Brownian particles which is analytically solvable for one-dimensional space with harmonic coupling. Each light mass particle (thick dot) is linked to at least one of the Brownian particles (filled disks) with Hookean springs (dashed lines). (b) Langevin model of two Brownian particles. Unlike the Hamiltonian model, each light mass particle receives the random force and frictional force from the background (shaded zone) and its inertia is ignored.