  Quantum fields are known to violate all the pointwise energy conditions of
classical general relativity. We review the subject of quantum energy
inequalities: lower bounds satisfied by weighted averages of the stress-energy
tensor, which may be regarded as the vestiges of the classical energy
conditions after quantisation. Contact is also made with thermodynamics and
related issues in quantum mechanics, where such inequalities find analogues in
sharp Gaarding inequalities.
