Heat Dissipation from Brownian Particles under Hydrodynamic Interactions
  We study the non-equilibrium thermodynamics of single Brownian macromolecules immersed in water solvent. They are under both a hydrodynamic interaction and a feedback control on their movement by an external agent. The macromolecules are described by a Langevin equation with a multiplicative noise. Work done by the macromolecules on the water solvent is dissipated as heat. Thus, the heat is expressed as the integration of an interacting force between the macromolecules and the water solvent along the position space trajectories of the macromolecules. This integration is stochastic due to the Brownian motion of the macromolecules. We show that the Stratonovich prescription of the integration is the unique physical choice. We also show that thermodynamic quantities such as heat, work, and entropy production, are derived without any ambiguity if both a diffusion matrix and external feedback control are known as priori. 
Kyung Hyuk Kim