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One of the pre-existing conditions of the story is a world 75-100 years from now where no viable source of energy comparable to fossil fuels has been found to replace the energy density of fossil fuels.
In this model, I feel that the loss of access to concentrated and relatively low-cost energy will have severe impacts on manufacturing processors. The high cost of energy will be reflected in the cost to the consumer for the processing power. This increase in cost will, more likely than not, decrease the demand for chips. The decrease in demand will provide a feedback loop which will require further price increase to offset volume of sales.
Chips would necessarily require the lowest amount of energy possible in their manufacture in order to retain the volumes required to economically maintain production
What sort of processors would fit into such a economic model, and what processor system, if any, would be the precursors of such a line of computing technology?"