Towards a physical theory of computer science.

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Experience seems to suggest that whenever we want to compute something, then we need to use some energy to do so. This could be the metabolic energy of our brains, electricity in the case of electronic computers or perhaps the energy stored in a spring in the case of mechanical calculating machines. Precisely how much energy a computation consumes depends on the specifics of the hardware used. An intriguing question one may ask is: For any given computation, what is the minimal amount of energy required to perform it, independently of any assumptions about the hardware? Partially, this question has been answered in the 1980s with a surprising result: In principle, computation can be performed with no energy expenditure all. This insight comes with an important caveat. The zero energy limit can only be reached if one is prepared to wait for an infinite amount of time for the computation to complete. In practice, this is clearly not useful. Computations that complete within a finite time, on the other hand, require a positive amount of energy to be expended. It follows that there must be a non-zero lower limit to the power consumption of such computations. Currently, it remains an open question what this limit is. The objective of this discipline hopping project is to establish rigorous physical models of computation so as to probe their minimal energy requirements. Specifically, the project will use newly developed methods in non-equilibrium statistical mechanics and apply them to concepts from theoretical computer science. The project will allow the PI to spend 4 months with the group of Prof. Massimiliano Esposito at the University of Luxembourg. There he will be able to acquire state of the art technical skills in stochastic thermodynamics, which will enable him to complete the project described here and to initiate a research programme aimed at establishing the physical limits of computing. The main outcome of the project will be a series of models that describe the physical limits to power consumption of computations.The topic of the project is of high societal relevance. Computing related activities now account for more than 10% of the total energy consumption globally. It is reasonable to assume that the absolute power consumption due to computation will grow exponentially in the future in line with economic growth. This is unsustainable and there needs to be a radical improvement of the efficiency of computers. Currently, such improvements are mainly driven by incremental hardware and software optimisations. In order to sustain an exponentially growing demand for computation, game changing new energy efficient technologies are required that operate at ultra-low power, close to the limit of what is possible. While this project will not directly lead to such new technologies, it will provide a deep understanding of the causes of energy dissipation in computation. As such it will underpin future engineering efforts aimed at finding solutions to the current energy crisis in computing. Importantly, the results of this project will also provide a benchmark to assess the energy efficiency of current hardware technologies against the theoretical optimum.