For 10 points, identify this function from statistical mechanics that describes the macroscopic properties of a thermodynamic system, which is symbolized Z.
N-point correlation functions can be calculated by differentiating this function N times with respect to the auxiliary function J. This function of a system of noninteracting particles composed of N subsystems can be written as the product of these for each subsystem, but if each subsystem is composed of identical particles, that total must be divided by N factorial to resolve the Gibbs paradox. The free energy for any particular ensemble is proportional to the (*) natural log of this function for that system. In a canonical ensemble, it is defined as the sum over microstates of the exponential function of quantity negative energy of microstate multiplied by thermodynamic beta. This function normalizes the Boltzmann distribution. For 10 points, identify this function from statistical mechanics that describes the macroscopic properties of a thermodynamic system, which is symbolized Z.
N-point correlation functions can be calculated by differentiating this function N times with respect to the auxiliary function J. This function of a system of noninteracting particles composed of N subsystems can be written as the product of these for each subsystem, but if each subsystem is composed of identical particles, that total must be divided by N factorial to resolve the Gibbs paradox.
partition function [or Z before mentioned]