Task: Text Categorization
Input (English): Performing a Wick rotatition of the time coordinate reduces the Feynman kernel to a functional which is similar to this quantity. The symmetry number is an overcounting correction factor that appears along with some power of the rotation temperature in the denominator for ones representing rotational energies. Its value for a system composed of several subsystems equals the product of its values for the subsystems, which implies that the Helmholtz free energy is additive over subsystems since the Helmholtz free energy is proportional to its logarithm. This quantity can also be thought of as a normalization constant since it is simply the integral over all states of the degeneracy factor times e to the negative beta times the energy of that microstate. For 10 points, name this quantity whose "canonical" form simply equals the sum over states of Boltzmann factors, and describes the macroscopic properties of a thermodynamic system.
Output (English): Science