# Selected Topics in Theoretical Physics from Quantum Null Energy Condition to Black Hole Thermodynamics

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The quantum null energy condition (QNEC) is a quantum generalization of the null energy condition which gives a lower bound on the null energy in terms of the second derivative of the von Neumann entropy or entanglement entropy of some region with respect to a null direction. The QNEC states that

It has been argued that using the Weyl tensor,

Typically, the entropy of an isolated system in equilibrium is calculated by counting the number of accessible microstates, or in more general cases by using the Gibbs formula. In irreversible processes entropy spontaneously increases and this is understood from statistical arguments. In Chapter ref{C:RR}, we propose a new definition of entropy directly based on the level of irreversibility of a process. This formulation agrees in first approximation with the usual methods of calculating entropy and can be readily applied in the case of a black hole in the semiclassical regime.