Calculation of absolute partition functions is impossible and unnecessary

5 Calculation of absolute partition functions is impossible and unnecessary 

It is noteworthy that a statistical mechanical calculation of absolute values of entropy or free energy is not required for determination of thermodynamic properties of matter. The functional dependence of the partition function on macroscopic properties, such as the total mass, volume, and temperature of the system, is sufficient to derive equations of state, internal energies, and heat capacities. For example, knowledge that the ideal gas partition function scales as is adequate to define and explain the ideal gas equation of state. 

Entropies, free energies, and chemical potentials are typically needed in relative terms, as differences between distinct macroscopic states. For example, the sign of the entropy change provides information on the direction in which a change of state process will spontaneously move. Nonetheless, it is impossible to determine an actual value for the absolute entropy or free energy of a macroscopic system. There are at least two reasons. 

from a physical perspective, it is not feasible to account for absolutely all degrees of freedom of a system in calculation of a partition function. Taking into account all subatomic degrees of freedom is impractical. Approximations such as the Born-Oppenheimer approximation that the nucleus of atoms is at the ground state are then indispensable, but the constant contribution to the total partition function is arbitrary. 

Second, calculation of the actual value of a partition function is intractable. For an ideal gas, the NVT ensemble partition function is 

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