  We investigate general structure of Landau free energy for stabilizing a
novel superconducting state with both even-frequency and odd-frequency
components in gap function. On the basis of the Luttinger-Ward functional, we
elucidate an emergent mixing between different "parities" in time. The simplest
case of the conventional s-wave singlet mixed with the odd-frequency triplet
state under broken time-reversal symmetry is examined to demonstrate the
anomalous structure of the free-energy functional. The induced odd-frequency
component alters behaviors of physical quantities from those obtained by
neglecting the odd-frequency component. The novel mixed state may also be
relevant to strong-coupling superconductivity coexisting with ferromagnetism.
