  We develop a Landauer-B\"uttiker theory of entropy evolution in
time-dependent strongly coupled electron systems. This formalism naturally
avoids the problem of system-bath distinction caused by the strong
hybridization of central system and surrounding reservoirs. In an adiabatic
expansion up to first order beyond the quasistatic limit, it provides a clear
understanding of the connection between heat and entropy currents generated by
time-dependent potentials and shows their connection to the occurring
dissipation. Combined with the work required to change the potential, the
developed formalism provides a full thermodynamic description from an outside
perspective, applicable to arbitrary non-interacting electron systems.
