This quantity is conjugate to the chemical potential.
For Bose-Einstein condensates, this value is proportional to fugacity over quantity 1 minus fugacity. In general, its expectation value is the negative of fugacity times change in the grand potential over fugacity. The operator corresponding to this quantity is the product of the creation and annihilation operators. Allowing this value to be variable generalizes the Boltzmann distribution to the Gibbs distribution. This quantity is conjugate to the chemical potential. By subtracting b times this value from volume, the van der Waals equation corrects the ideal gas law, which states it as equal to P times V over quantity k times T. For 10 points, name this property of a system often symbolized N, equal to Avogadro's number times the number of moles.
For Bose-Einstein condensates, this value is proportional to fugacity over quantity 1 minus fugacity.
particle number [or obvious equivalents; prompt on N; accept number of moles due to the van der Waals clue]