Universal upper bound on the entropy-to-energy ratio for bounded systems

The speed with which a physical device can process information is limited by its energy.

“In particular, the speed with which a physical device can process information is limited by its energy 11 -26 and the amount of information that it can process is limited by the number of degrees of freedom it possesses 5 -40 .”

The laws of quantum mechanics determine the maximum rate at which a system with spread in energy ΔE can move from one distinguishable state to another.

“The problem of how much energy is required for information processing was first investigated in the context of communications theory by Levitin 11 -16 , Bremermann 17 -19 , Beckenstein 20 -22 and others, who showed that the laws of quantum mechanics determine the maximum rate at which a system with spread in energy ∆ E can move from one distinguishable state to another.”

As ordinary matter obeys the Bekenstein bound, k_B RE/ħcS > 1/2π, as one compresses the computer t_com/t_flip ≈ k_B RE/ħcS will remain greater than one, so the operation will still be somewhat parallel.

“As ordinary matter obeys the Beckenstein bound 20 -22 , k B RE/ ¯ hcS > 1 / 2 π , however, as one compresses the computer t com /tfl ip ≈ k B RE/ ¯ hcS will remain greater than one: i.e., the operation will still be somewhat parallel.”

The serial nature of computation at the black-hole limit can be deduced from the fact that black holes attain the Bekenstein bound, k_B RE/ħcS = 1/2π.

“As noted above, the serial nature of computation at the black-hole limit can be deduced from the fact that black holes attain the Beckenstein bound 20 -22 , k B RE/ ¯ hcS = 1 / 2 π .”