  Thermodynamic properties of Robin quantum well with extrapolation length
$\Lambda$ are analyzed theoretically both for canonical and two grand canonical
ensembles with special attention being paid to situation when energies of one
or two lowest-lying states are split-off from rest of spectrum by large gap
that is controlled by varying $\Lambda$. For single split-off level, which
exists for the geometry with equal magnitudes but opposite signs of Robin
distances on confining interfaces, heat capacity $c_V$ of canonical averaging
is a nonmonotonic function of temperature $T$ with its salient maximum growing
to infinity as $\ln^2\Lambda$ for decreasing to zero extrapolation length and
its position being proportional to $1/(\Lambda^2\ln\Lambda)$. Specific heat per
particle $c_N$ of Fermi-Dirac ensemble depends nonmonotonically on temperature
too with its pronounced extremum being foregone on $T$ axis by plateau whose
value at dying $\Lambda$ is $(N-1)/(2N)k_B$, with $N$ being a number of
fermions. Maximum of $c_N$, similar to canonical averaging, unrestrictedly
increases as $\Lambda$ goes to zero and is the largest for one particle. Most
essential property of Bose-Einstein ensemble is a formation, for growing number
of bosons, of sharp asymmetric shape on the $c_N-T$ characteristics that is
more protrusive at the smaller Robin distances. This cusp-like structure is a
manifestation of the phase transition to the condensate state. For two
split-off orbitals, one additional maximum emerges whose position is shifted to
colder temperatures with increase of energy gap between these two states and
their higher-lying counterparts and whose magnitude approaches
$\Lambda$-independent value. All these physical phenomena are qualitatively and
quantitatively explained by variation of energy spectrum by Robin distance.
