  The fundamental insight into Brownian motion by Einstein is that all
substances exhibit continual fluctuations due to thermal agitation balancing
with the frictional resistance. However, even at thermal equilibrium,
biological activity can give rise to non-equilibrium fluctuations that cause
``active diffusion" in living cells. Because of the non-stationary and
non-equilibrium nature of such fluctuations, mean square displacement analysis,
relevant only to a steady state ensemble, may not be the most suitable choice
as it depends on the choice of the ensemble; hence, a new analytical method for
describing active diffusion is desired. Here we discuss the stochastic
energetics of a thermally fluctuating single active diffusion trajectory driven
by non-thermal random forces. Heat dissipation, usually difficult to measure,
can be estimated from the active diffusion trajectory; guidelines on the
analysis such as criteria for the time resolution and driving force intensity
are shown by a statistical test. This leads to the concept of an
``instantaneous diffusion coefficient" connected to heat dissipation that may
be used to analyse the activity and molecular transport mechanisms of living
systems.
