The Maxwell–Boltzmann distribution is a hallmark of statistical physics in thermodynamic
equilibrium linking the probability density of a particle’s kinetic energies to the temperature
of the system that also determines its configurational fluctuations. This unique relation is
lost for Hot Brownian Motion, e.g., when the Brownian particle is constantly heated to
create an inhomogeneous temperature in the surrounding liquid. While the fluctuations of
the particle in this case can be described with an effective temperature, it is not unique for
all degrees of freedom and suggested to be different at different timescales. In this work,
we report on our progress to measure the effective temperature of Hot Brownian Motion in
the ballistic regime. We have constructed an optical setup to measure the displacement of
a heated Brownian particle with a temporal resolution of 10 ns giving a corresponding
spatial resolution of about 23 pm for a 0.92 μm PMMA particle in water. Using a goldcoated
polystyrene (AuPS) particle of 2.15 μm diameter we determine the mean squared
displacement of the particle over more than six orders of magnitude in time. Our data
recovers the trends for the effective temperature at long timescales, yet shows also clear
effects in the region of hydrodynamic long time tails
