  Applying the first and generalised second laws of thermodynamics for a
realistic process of near critical black hole formation, we derive an entropy
bound, which is identical to Bekenstein's one for radiation. Relying upon this
bound, we derive an absolute minimum mass $\sim0.04 \sqrt{g_{*}}m_{\rm Pl}$,
where $g_{*}$ and $m_{\rm Pl}$ is the effective degrees of freedom for the
initial temparature and the Planck mass, respectively. Since this minimum mass
coincides with the lower bound on masses of which black holes can be regarded
as classical against the Hawking evaporation, the thermodynamical argument will
not prohibit the formation of the smallest classical black hole. For more
general situations, we derive a minimum mass, which may depend on the initial
value for entropy per particle. For primordial black holes, however, we show
that this minimum mass can not be much greater than the Planck mass at any
formation epoch of the Universe, as long as $g_{*}$ is within a reasonable
range. We also derive a size-independent upper bound on the entropy density of
a stiff fluid in terms of the energy density.
