End-directed evolution and the emergence of energy-seeking behavior in a complex system

Self-organization in a voltage-driven nonequilibrium system, consisting of conducting beads immersed in a viscous medium, gives rise to a dynamic tree structure that exhibits wormlike motion. The complex motion of the beads driven by the applied field, the dipole-dipole interaction between the beads and the hydrodynamic flow of the viscous medium, results in a time evolution of the tree structure towards states of lower resistance or higher dissipation and thus higher rates of entropy production. Thus emerges a remarkably organismlike energy-seeking behavior. The dynamic tree structure draws the energy needed to form and maintain its structure, moves to positions at which it receives more energy, and avoids conditions that lower available energy. It also is able to restore its structure when damaged, i.e., it is self-healing. The emergence of energy-seeking behavior in a nonliving complex system that is extremely simple in its construct is unexpected. Along with the property of self-healing, this system, in a rudimentary way, exhibits properties that are analogous to those we observe in living organisms. Thermodynamically, the observed diverse behavior can be characterized as end-directed evolution to states of higher rates of entropy production.

Figure 1

Self-organization of a dynamic tree structure in a voltage-driven system. (a) Schematic of the basic setup in which conducting beads, placed in 60 ml of oil, are subjected to voltage $V=26\mathrm{k}\mathrm{V}$ across the source and the ground ring electrode. (b)–(e) Evolution of the tree structure at four time points. (e) With swaying branches, the tree as a whole can move while maintaining its contact with the ring. (f) Rate of entropy production Σ (in mJ/Ks) during formation of the tree structure. When the tree makes contact with the ground electrode, there is a sharp increase in Σ.

Figure 2

Entropy production Σ in the system. (a) Plot of Σ as a function of the voltage for $N_{\mathrm{beads}}=20$; at a given voltage, Σ is on the lower curve (preformation) but jumps to the upper curve when the tree makes contact with the ground electrode (postformation). (b) For a fixed voltage of 26 kV the magnitude of the Σ jump depends on the number of beads. Error bars are equal to ±1 standard error.

Figure 3

Energy-seeking motion of the tree. (a) With an off-center source electrode, the base of the tree is confined by two gates to a state of lower Σ (lower panel); when a gate is opened, the tree moves quickly to increase $\mathrm{\Sigma }$ (see video 2 in Ref. [14]). (b) When the tree is moved to a location with lower Σ by tilting the system (around 580 s) by 5° for 5 s $\left(t=577–582\right)$, it moves back to the state with higher Σ.

Figure 4

Plot of Σ as a function tree length. (a) With a fixed total number of beads $N_{\mathrm{beads}}=20$, trees of varying length were constructed (e.g., ten two-bead trees, or five four-bead trees). Here Σ increases when there are fewer but longer trees. A single 20-bead tree has the highest Σ. (b) Results of a perturbation of a set of trees of different length. When a system of smaller trees is perturbed, they reform into longer trees (e.g., two-bead trees regroup to form four-bead trees). Error bars are equal to ±1 standard error.