Ultimate Physical Limits to Computation

Computers are physical systems: the laws of physics dictate what they can and cannot do. In particular, the speed with which a physical device can process information is limited by its energy and the amount of information that it can process is limited by the number of degrees of freedom it possesses. Here I explore the physical limits of computation as determined by the speed of light c , the quantum scale ℏ and the gravitational constant G . As an example, I put quantitative bounds to the computational power of an ‘ultimate laptop’ with a mass of one kilogram confined to a volume of one litre.