  This paper revisits the classical problem of representing a thermal bath
interacting with a system as a large collection of harmonic oscillators
initially in thermal equilibrium. As is well known the system then obeys an
equation, which in the bulk and in the suitable limit tends to the
Kramers-Langevin equation of physical kinetics. I consider time-dependent
system-bath coupling and show that this leads to an additional harmonic force
acting on the system. When the coupling is switched on and switched off rapidly
the force has delta-function support at the initial and final time, an effect
that has been observed previously. I further show that the work and heat
functionals as recently defined in stochastic thermodynamics at strong coupling
contain additional terms depending on the time derivative of the system-bath
coupling. I discuss these terms and show that while they can be very large if
the system-bath coupling changes quickly they only give a finite contribution
to the work that enter in Jarzynski's equality. I also discuss that these
corrections to standard work and heat functionals provide an explanation for
non-standard terms in the change of the von Neumann entropy of a quantum bath
interacting with a quantum system found in an earlier contribution (Aurell \&
Eichhorn, 2015).
