  Thermodynamic entropy is determined by a heat measurement through the
Clausius equality. The entropy then formalizes a fundamental limitation of
operations by the second law of thermodynamics. The entropy is also expressed
as the Shannon entropy of the microscopic degrees of freedom. Whenever an
extension of thermodynamic entropy is attempted, we must pay special attention
to how its three different aspects just mentioned are altered. In this paper,
we discuss possible extensions of the thermodynamic entropy.
