Hydrodynamically Consistent Many-Body Harada-Sasa Relation

The effect of hydrodynamic interactions on the nonequilibrium stochastic dynamics of particles-arising from the conservation of momentum in the fluid medium-is examined in the context of the relationship between fluctuations, response functions, and the entropy production rate. The multiplicative nature of the hydrodynamic interactions is shown to introduce subtleties that preclude a straightforward extension of the Harada-Sasa relation. A generalization of the definitions involved in the framework is used to propose a new form of the relation applicable to systems with hydrodynamic interactions. The resulting framework will enable characterization of the nonequilibrium properties of living and active matter systems, which are predominantly in suspensions.