The thermodynamic entropy production is evaluated in different parts of the attractor of two representative reactive models giving rise to periodic and chaotic behavior. The variability patterns observed as the system runs over the attractor are compared with the variability of the indicators of the intrinsic complexity of the dynamics such as the local Lyapunov exponents, a local generalization of Kolmogorov entropy, and the linear velocity along the trajectory. The analysis reveals some unexpected correlations. In particular, it appears that the largest span of values of entropy production, including in many cases the maximum value itself, occurs at stages during which the dynamics is dominated by stability (local Kolmogorov entropy is close to zero). Strong correlations are also shown to exist between high dissipation and high values of the linear velocity.