Thousands of numerical solutions of an optimal control problem for plug flow reactors were found to give, what we call a "highway in the reactors' state space". The problem was to find the heat transfer strategy which minimise the entropy production in reactors with fixed chemical conversion. The control variable was always the temperature of the heating/cooling medium along the reactor. The highway represents the most energy efficient way to travel far in state space. Such highways were studied for five reactor systems, endothermic and exothermic ones. Numerical analysis showed that the reactor highway is characterised by approximately constant thermodynamic driving forces/local entropy production for reasonable process intensities. Each solution represents a compromise between the entropy production of reactions, heat transfer and frictional flow (pressure drop). The solutions enter and leave the highway at different positions depending on how far from the highway their initial and final destinations are. Knowledge about the nature of the highway, e.g. when the reactor operates in a reaction mode or a heat transfer mode, may be important for energy efficient reactor design. The theoretical formulation of the optimisation problem is valid for plug flow as well as batch reactors. We showed that important results in literature like the Spirkl-Ries quantity, the theorems of equipartition of entropy production and equipartition of forces are contained in our general formulation. The numerical results showed that the analytical results are good approximations to the optimum also in problems where they do not apply in a strictly mathematical sense. (c) 2005 Elsevier Ltd. All rights reserved.