Communication can often be exchanged with computation in control systems. A car's computer needing to know the speed can either get the data from the speed sensor over the vehicle's communication network (bus); or it can calculate the speed from the initial speed, the history of throttle commands, using the laws of physics driving the car. In a fully deterministic world with powerful enough computers, communication may be redundant. In the real world, the degree of uncertainty in the physics can say something about the level of communication necessary. Quantifying this communication need can help principled design and allocation of network bandwidth and other resources in vehicles and other control systems.
Uncertainty or lack of information is usually measured by entropy of some flavor. Claude Shannon developed a definition of entropy in the context of engineering telephone networks. That definition uses probability distributions, not coincidentally, capturing noise in telephone channels. In contrast, topological entropy, used in studying evolution of worstcase uncertainty in safety-critical systems, does not use probabilities at all. Instead, it measures the rate of growth of uncertainty in a system's state with time. Topological entropy of a stable system like a pendulum will be smaller than that of an unstable system like an inverted pendulum.
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