  With the help of the coherent states' basis we establish an interesting
connection among i) the so-called Wehrl entropy, ii) Fisher's information
measure $I$, and iii) the canonical ensemble entropy for the one-dimensional
quantum harmonic oscillator (HO). We show that the contribution of the excited
HO spectrum to the mean thermal energy is given by $I$, while the pertinent
canonical partition function is given by another Fisher measure: the so-called
shift invariant one, minus the HO's ground state energy.
  Our findings should be of interest in view of the fact that it has been shown
that the Legendre transform structure of thermodynamics can be replicated
without any change if one replaces the Boltzmann-Gibbs-Shannon entropy by
Fisher's information measure [{\it Physical Review E} {\bf 60}, 48 (1999)]. New
Fisher-related uncertainty relations are also advanced.
