Renyi Entropy and Free Energy

The Renyi entropy is a generalization of the usual concept of entropy which depends on a parameter q. In fact, Renyi entropy is closely related to free energy. Suppose we start with a system in thermal equilibrium and then suddenly divide the temperature by q. Then the maximum amount of work the system can perform as it moves to equilibrium at the new temperature divided by the change in temperature equals the system's Renyi entropy in its original state. This result applies to both classical and quantum systems. Mathematically, we can express this result as follows: the Renyi entropy of a system in thermal equilibrium is without the 'q(-1) -derivative' of its free energy with respect to the temperature. This shows that Renyi entropy is a q-deformation of the usual concept of entropy.

Automated summary

The Renyi entropy is a generalization of entropy that depends on the parameter q and is closely related to free energy. When a system is in thermal equilibrium and the temperature changes, the Renyi entropy can be expressed as the derivative of the system's free energy with respect to temperature.