Synergistic action in colloidal heat engines coupled by non-conservative flows

Colloidal heat engines are model systems to analyze mechanisms of transduction of heat to work at the mesoscale. While engines developed hitherto were realized using conservative potentials and operated in isolation, biological micromotors - their real counterparts - seldom perform under such simplifications. Here, we examine thermodynamics beyond such idealizations by constructing a pair of engines from two colloidal microspheres in optical traps at close separation. We demonstrate that at such proximity, non-conservative scattering forces that were hitherto neglected affect the particle motion. Hydrodynamics generated while dissipating these are hindered by the microsphere in the adjacent trap and energy that was otherwise rejected into the medium gets reused. Thus, despite being in contact with the same reservoir, the particles are driven out of equilibrium and can exchange energy, allowing cooperative behavior. Leveraging this in a manner analogous to microswimmers and active Brownian particles that utilize such flows to enhance propulsion, we construct two colloidal engines in close proximity. To estimate thermodynamic quantities, we develop a minimal model that is appropriate in the asymptotic limit and is similar to active Brownian particles. While complete theoretical frameworks to understand such scenarios remain to be developed, results based on our model demonstrate the intuitive idea that a pair of Stirling engines at close proximity outperform those that are well separated. Although these results explore the simplest case of two Stirling engines, the concepts unraveled could aid in designing larger collections akin to biological systems.