Acoustic Dip in the Effective Temperature of Hot Brownian Motion

This paper presents a theoretical study on hot Brownian motion in compressible solvents. The authors demonstrate that finite sound speed qualitatively changes the frequency-dependent effective temperature in the kinetic regime, extending beyond the conventional incompressible solvent assumption. By solving the compressible fluctuating-hydrodynamic problem for a heated sphere, they reveal an acoustic dip feature in the effective temperature spectrum. The work provides new insights into non-equilibrium thermodynamics and fluctuation-dissipation relations in thermal fluids.