  In this paper we analyze the entropy and entropy production of a non-isolated
quantum system described within the quantum Brownian motion framework. This is
a very general and paradigmatic framework for describing non-isolated quantum
systems and can be used in any kind of coupling regime. We start by considering
the application of von Neumann entropy to an arbitrarily damped quantum system
making use of its reduced density operator. We argue that this application is
formally valid and develop a path integral method to evaluate that quantity
analytically. We apply this technique to a harmonic oscillator in contact with
a heat bath and obtain an exact form for its entropy. Then we study the entropy
production of this system and enlighten important characteristics of its
thermodynamical behavior on the pure quantum realm and also address their
transition to the classical limit.
