Non-equilibrium statistical mechanics of the heat bath for two Brownian particles

Caterina De Bacco ¹ Fulvio Baldovin ² Enzo Orlandini ² Ken Sekimoto ^{3, 4}

Physical Review Letters, American Physical Society, 2014, 112, pp.180605

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. Non-local thermal fluctuation 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 nano-scale physics.

• 1. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
• 2. Dipartimento di Fisica e Astronomia G. Galilei and Sezione I NFN
• 3. MSC – Matière et Systèmes Complexes
• 4. LPCT – Laboratoire de Physico-Chimie Théorique