Is information something real?



Normally one speaks of living things as beings that consume energy to survive and proliferate. This is of course not correct; energy is conserved, and cannot be consumed. Living beings intercept entropy flows; they use low-entropy sources of energy and emit high entropy forms of the same energy (body heat).

Can we burn information as fuel? Consider a really frugal digital memory tape, with one atom used to store each bit:

The position of a single ideal gas atom denotes a bit. If it is in the top half of a partitioned box, the bit is one, otherwise it is zero. The side walls of the box are pistons, which can be used to set, reset, or extract energy from the stored bits. The numbers above the boxes are not a part of the tape, they just denote what bit is stored in a given position.

The tape is a series of boxes, with each box containing one ideal gas atom. The box is split into two equal pieces by a removable central partition. If the atom is in the top half of the box, the tape reads one; if it is in the bottom half the tape reads zero. The side walls are frictionless pistons that may be used to push the atom around. If we know the atom position in the n-th box, we can move the other side wall in, remove the partition, and gradually retract the piston to its original position destroying our information about where the atom is, but extracting useful work.

Extracting energy from a known bit is a three-step process: compress the empty half of the box, remove the partition, and retract the piston and extract PdV work out of the ideal gas atom. (One may then restore the partition to return to an equivalent, but more ignorant, state.) In the process, one loses one bit of information (which side of the the partition is occupied).

A memory tape can therefore be used to power an engine. If the engine knows or can guess the sequence written on the tape, it can extract useful work in exchange for losing that information.


Statistical Mechanics,  J. Sethna

This is an old post that is bouncing around, but it’s not actually true.  The memory tape is not powering the engine, the gas in the chamber is.  Or, if your gas is in thermal contact with a heat reservoir with some temperature T, you’re extracting work from the reservoir (T ln 2 of work).  

What you have done is run an engine without a cold reservoir.  Which is interesting!  The relationship to information is entropy, not information.  We can’t burn information as fuel, but we can use information to extract work we’d otherwise not be able to.  This seems maybe really pedantic, but it’s super important. The correspondence between information and entropy is quite deep. 

Since this post is getting some attention, comments and questions, I suggest you guys have a look at the reference at the bottom of the text, that will explain the matter better than any tumblr post.