Research Article

Physical Portrayal of Computational Complexity

Figure 1

Computation is considered as a dissipative process. The input as an influx of energy disperses from the input interface (top) through the network that evolves during the computation, according to the 2nd law of thermodynamics by dissipative transitions that acquire high (blue) and yield low (red) density in energy, toward the stationary state (bottom). Reversible transitions, that is, conserved currents (purple), do not bring about changes of state and do not advance the computation. Driving forces (free energy between the nodes) and flows (between the nodes) are inseparable when there are additional degrees of freedom ( 𝑛 3 ), that is, alternative yet interdependent paths for the dissipative processes to proceed along. Then the flows are intractable and the corresponding algorithmic execution is nondeterministic.
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