The paper analyzes the entropy of a system composed by an arbitrary number of
indistinguishable particles at the equilibrium, defining entropy as a function
of the quantum state of the system, not of its phase space representation. Our
crucial observation is that the entropy of the system is the Shannon entropy of
the random occupancy numbers of the quantum states allowed to system's
particles. We consider the information-theoretic approach, which is based on
Jaynes' maximum entropy principle, and the empirical approach, which leads to
canonical typicality in modern quantum thermodynamics. In the
information-theoretic approach, the occupancy numbers of particles' quantum
states are multinomially distributed, while in the empirical approach their
distribution is multivariate hypergeometric. As the number of samples of the
empirical probability tends to infinity, the multivariate hypergeometric
distribution tends to the multinomial distribution. This reconciles, at least
in the limit, the two approaches. When regarded from the perspective of quantum
measurement, our analysis suggests the existence of another kind of
subjectivism than the well-known subjectivism that characterizes the maximum
entropy approach. This form of subjectivity is responsible for the collapse of
entropy to zero after the quantum measurement, both in the
information-theoretic and in the empirical approaches