  In this study, we model a harmonic oscillator that enters an interferometer
partially coupled to a thermal bath of oscillatory fields by employing a
Brownian-type Lindblad master equation. More specifically, we investigate the
dynamics and the variations of the thermodynamic quantities of the system at
different temperatures. We recognize that although the system can remain
coherent during its interaction with the thermal bath in the low-temperature
limit, the system's entropy production violates the Clausius inequality.
Furthermore, we argue that the system's coherence is the source of this
violation, rather than the entanglement degree of system-environment, as
reported in previous studies.
