Task: Text Categorization
Input (English): In quantum mechanical systems, this can be defined as the negative trace of the density matrix multiplied by the log of the density matrix. For a gas of photons, this quantity is directly proportional to the total number of photons. Pressure can be calculated as temperature times the partial derivative of this quantity with respect to volume. The Sackur-Tetrode equation gives the value of this for an ideal gas, while inverse temperature is equal to the derivative of this with respect to energy. It is generally defined as Boltzmann's constant times the logarithm of the number of microstates. FTP, identify this quantity that always increases according to the 2nd Law of Thermodynamics.
Output (English): Science