Hinton and Zemel (zeh-mahl) used a function based on this quantity to compute recognition weights used to train an autoencoder. Two-sided estimation is used by the Bennett's acceptance ratio method to approximate this quantity. One relation states that this function for a liquid system is bounded above by a reference plus the difference between the Hamiltonians of the true and reference systems; that is the Bogoliubov (buh-GOAL-you-bahv) inequality. This quantity is minimized when a system is touching a thermal reservoir, and it is equal to (*) negative Boltzmann's constant times temperature times the natural log of the partition function. This state function is the 
Hinton and Zemel (zeh-mahl) used a function based on this quantity to compute recognition weights used to train an autoencoder. Two-sided estimation is used by the Bennett's acceptance ratio method to approximate this quantity. One relation states that this function for a liquid system is bounded above by a reference plus the difference between the Hamiltonians of the true and reference systems; that is the Bogoliubov (buh-GOAL-you-bahv) inequality. This quantity is minimized when a system is touching a thermal reservoir, and it is equal to (*) negative Boltzmann's constant times temperature times the natural log of the partition function. This state function is the maximum amount of work obtainable from a reversible process and can be expressed as internal energy minus entropy times temperature. For 10 points, name this non-Gibbs free energy.
Hinton and Zemel (zeh-mahl) used a function based on this quantity to compute recognition weights used to train an autoencoder.
Helmholtz free energy [prompt on partial answers like free energy or energy]