Figure 3.

Illustration of three different cases in which an internal process alters the entropy budget of the system (left diagrams) and the entropy production σ_ab owing to the heat flux F_ab, the increase of total entropy production Δσ_tot, and the entropy of the system S, as functions of the heat flux F_ab. (a) Case (i) allows for two types of heat transfer between boxes a and b. Flux F_c operates with a fixed conductivity and the flux F_ab is taken to have degrees of freedom so that its magnitude can vary. The fluxes across the system boundary are fixed in terms of their energy and entropy. Since F_out is proportional to T_b but fixed in steady state to F_in, T_b is fixed to a value of F_in/k_b. (b) Case (ii) extends case (i) in which it allows flexibility in the entropy export by flux F_out from the system. The flux F_c is neglected in this set-up. (c) Case (iii) extends case (ii) in which it allows flexibility in the influx F_in as well. The graphs on the right show the resulting sensitivities of the system's entropy budget to the heat flux F_ab of entropy production σ_ab owing to the heat flux F_ab, the increase in total entropy production by the system Δσ_tot compared with the total entropy production with F_ab = 0, and the entropy of the system S. The grey area in the lowest graph indicates a region in which a particular value of heat flux F_ab can result from a higher value of F_in and a comparatively lower temperature gradient or a lower value of F_in and a higher temperature gradient.