  The reliability of physical theories depends on whether they agree with well
established physical laws. In this work, we address the compatibility of the
Hamiltonian formulation of linear-response theory with the Second Law of
Thermodynamics. In order to do so, we verify three complementary aspects often
understood as statements of the Second Law: 1. No dissipation for quasistatic
process; 2. Dissipation for finite-time processes; 3. Positive entropy
production rate. Our analysis focus on two classes of nonequilibrium isothermal
processes: slowly-varying and finite-time but weak ones. For the former, we
show that these aspects are easily verified. For the later, we present
conditions for the achievement of the first two aspects. We also show that the
third one is not always verified, presenting an example based on Brownian
motion in which we observe negative values in the entropy production rate. In
particular, we compare linear-response and exact results for this example.
