  We formulate the thermofield dynamics for time-dependent systems by combining
the Liouville-von Neumann equation, its invariant operators, and the basic
notions of thermofield dynamics. The new formulation is applied to
time-dependent bosons and fermions by using the time-dependent annihilation and
creation operators that satisfy the Liouville-von Neumann equation. It is shown
that the thermal state is the time- and temperature-dependent vacuum state and
a general formula is derived to calculate the thermal expectation value of
operators.
