Fig. 3: Selection of states in a chain of three-state subsystems in a thermal gradient.
From: Dissipation-driven selection of states in non-equilibrium chemical networks
a Chain of three concatenated three-state chemical networks, each similar to the one in Fig. 1a. The orange circle indicates a subsystem belonging to the class R, with the fast transition on the right branch, while the blue circle indicates a subsystem whose fast transition is on the left branch (class L). b \({R}_{{C}_{{\rm{k}}}{\rm{B}}}\,=\,P({C}_{{\rm{k}}})/P(B)\) as a function of the states Ck. The selection of states does not depend only on their transitions being fast or slow with respect to the neighboring reactions, but on all rates of the network. Here kB = 1, T = 0.7, ΔT = 0.2, ΔEk ~ U([1, 10]), \({{\Delta }}{\epsilon }_{{\rm{slow}}}^{(i)} \sim U([3,6])\) and \({{\Delta }}{\epsilon }_{{\rm{fast}}}^{(i)} \sim U([2,3])\), where U is the uniform distribution. Each subsystem belongs to class L with probability p = 0.5, and to class R with probability 1 − p. Inset—\({R}_{{{\rm{C}}}_{{\rm{k}}}B}\) as a function of the species Ck for the same parameters as in the main panel, but p = 0.75. The predominance of subsystems belonging to the class R leads to a directional exponential growth.
