Task: Text Categorization
Input (English): Differentiating this quantity with respect to the auxiliary function can be used to find the Feynman amplitude, while performing a Wick rotation on a Feynman path integral creates a function analogous to this one. Partially differentiating it twice with respect to alpha is equal to the variance in the number of particles when beta and volume are constant. Multiplying its partial derivative with respect to volume at constant chemical potential and beta is equal to the pressure, while it serves as the normalizing constant for the Gibbs measure. This function is equal to the sum over all microstates of e raised to the negative beta times the energy of that microstate, and it is usually defined for a canonical ensemble. For 10 points, name this function, which can be used to express all the properties of a thermodynamical system.
Output (English): Science