  We explore an analogy between the thermodynamics of a free dissipative
quantum particle and that of an electromagnetic field between two mirrors of
finite conductivity. While a free particle isolated from its environment will
effectively be in the high-temperature limit for any nonvanishing temperature,
a finite coupling to the environment leads to quantum effects ensuring the
correct low-temperature behavior. Even then, it is found that under appropriate
circumstances the entropy can be a nonmonotonic function of the temperature.
Such a scenario with its specific dependence on the ratio of temperature and
damping constant also appears for the transverse electric mode in the Casimir
effect. The limits of vanishing dissipation for the quantum particle and of
infinite conductivity of the mirrors in the Casimir effect both turn out to be
noncontinuous.
