Reversible Computing @rev_comp

HYPRES and SUNY are also making amazing strides in reversible superconducting logics. #RevComp

Northrop Grumman is doing some beautiful work on reversible superconducting logic. #RevComp

All the leading-edge physicists already accepted that entropy is information long ago. It's surprising that anyone is still skeptical of it.

The development of quantum theory also vindicated Boltzmann, showing explicitly that atomic systems had a discrete set of distinct states.

Shannon's contribution was to apply Boltzmann's definition of entropy in the development of his mathematical theory of communication.

Claude Shannon, information theory pioneer, is sometimes credited with the insight that entropy is information, but Shannon cites Boltzmann.

Meanwhile, Ludwig Boltzmann realized entropy is a measure of information, S = k ln W, where W is the number of states. #ItsOnHisTombstone

Later thermodynamicists realized that Clausius' equation could be turned around and used as a definition of temperature, T= ΔQ/ΔS, as ΔQ→0.

Clausius def'd entropy (fr. Gk., "inner transformation") as the "equivalence value" S of quantity Q of heat dissipated at temp. T: S = Q/T.

Of course, the first experiments in the 1800s that led Rudolf Clausius to define entropy already are evidence that it doesn't go away.

A test of Landauer's principle (or the 2nd Law generally) thus amounts to checking that we haven't overlooked some hidden corner of reality.

Thus, Landauer's principle (and thermodynamics) are tautological if one defines "the universe" to include "everywhere information can go."

In other words, you could never finally prove that some information really disappeared - you could only say you didn't know where it went.

However, even then, one could argue that that "irreversible" universe is embedded in a larger reversible one where thermodynamics is true.

If this was not the case, entropy (and heat) could vanish from the universe and the laws of thermodynamics would not hold.

The function from "old state" to "new state" is mathematically injective, that is, one-to-one. No two predecessor states share a successor.

Landauer's principle follows directly from the fact that microscopic physical dynamics is reversible - it evolves injectively.

If you instead reversibly decompute a bit under control of other bits with which it's correlated, Landauer's principle does not apply.

However, Landauer's principle applies only to *oblivious* erasure - performed without reference to the information being erased.

Landauer clarified that erasure of known information generates entropy - this has been empirically tested. nature.com/news/the-unavo…