  A formal analogy of fluctuating diffusivity to thermodynamics is discussed
for messenger RNA molecules fluorescently fused to a protein in living cells.
Regarding the average value of the fluctuating diffusivity of such RNA-protein
particles as the analog of the internal energy, the analogs of the quantity of
heat and work are identified. The Clausius-like inequality is shown to hold for
the entropy associated with diffusivity fluctuations, which plays a role
analogous to the thermodynamic entropy, and the analog of the quantity of heat.
The change of the statistical fluctuation distribution is also examined from a
geometric perspective. The present discussions may contribute to a deeper
understanding of the fluctuating diffusivity in view of the laws of
thermodynamics.
