About the attraction of hot particles in a cold bath

Motivated by questions in biological physics, we consider a model in which different Brownian particles interact with different thermostats. Computer simulations show that hot particles (i.e., interacting with the hot bath) attract each other when placed in an environment of colder particles (i.e., interacting with the cold thermostat). This paper presents a simple calculation that sheds light on the physical nature of this attraction.