Electrical and Electronic Engineering - Theses

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Fundamental energy requirements of information processing and transmission
Angley, Daniel Michael ( 2015)
This thesis investigates fundamental limits on the energy required to process and transmit information. By combining physical laws, such as the second law of thermodynamics, with information theory, we present novel limits on the efficiency of systems that track objects, perform stochastic control, switch communication systems and communicate information. This approach yields results that apply regardless of how the system is constructed. While the energy required to perform an ideal measurement of a static state has no known lower bound, this thesis demonstrates that this is not true for noisy measurements or if the state is evolving stochastically. We derive new lower bounds on the energy required to perform such tracking tasks, including Kalman filtering. The goal of stochastic control is usually to reduce the entropy of the controlled system. This is also the task of a Maxwell demon, a thought experiment in which a device or being reduces the thermodynamic entropy of a closed system, violating the second law of thermodynamics. We demonstrate that the same arguments that `exorcise' Maxwell's demon can be used to find lower bounds on the energy consumption of stochastic controllers. We show that the configuration of a switching system in communications, that directs input signals to the desired outputs, can be used to store information. Reconfiguring the switch therefore erases information, and must have an energy cost of at least $k_B T \ln(2)$ per bit due to Landauer's principle. We then calculate lower bounds on the energy required to perform finite-time switching in a one-input, two-output MEMS (microelectromechanical system) mirror switch subject to Brownian motion, demonstrating that the shape of the potential that the switch is subject to affects both the steady-state noise and the energy required to change the configuration. Finally, by modifying Feynman's ratchet and pawl heat engine in order to perform communication instead of doing work, we investigate the efficiency of communication systems that operate solely using the temperature difference between two thermal reservoirs. The lower bound for the energy consumption of any communication system operating between two thermal reservoirs, with no channel noise and using equiprobable partitions of heat energy taken from these reservoirs, is found to be $\frac{T_H T_C}{T_H-T_C} k_B \ln(2)$, where $T_H$ and $T_C$ are the temperatures of the hot and cold reservoir, and $k_B$ is Boltzmann's constant.