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Suppose you have a Maxwell demon scenario where particles in a box get sorted out by a goblin so that the entropy of the box decreases. Landauer (1960) proposes that the net entropy loss would be compensated by the demon having to store and delete the information it knows about the system, however he doesn't elaborate about a process before the demon's storage capacity is reached yet heaving caused an entropy decrease in the box.

Would a plausible answer be that the informational entropy stored by the demon should be more than equal to the thermodynamic entropy extracted? Is it even justifiable by the second law to say that thermodynamical entropy can be compensated by informational entropy even if informational entropy itself is not physically stored in a way that would equate to the thermodynamical entropy extracted?

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There is an excellent discussion of responses to Maxwell's demon in this Wikipedia article. Basically, Maxwell's demon must use one or more of the following methods:

  1. An external power source - in which case the demon plus gas is no longer an isolated system and the second law of thermodynamics does not apply.
  2. A way of measuring molecular speeds via an irreversible process - in which case the increase in entropy due to the measuring process outweighs the decrease in entropy achieved by the demon .
  3. A way of measuring molecular speeds via a reversible process - in which case the demon must use a finite memory to remember its measurements, and the increase in entropy caused by erasing and reusing parts of this memory outweighs the decrease in entropy achieved by the demon.
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informational entropy itself is not physically stored in a way that would equate to the thermodynamical entropy extracted?

A 1 gram memory stick has billions of joules energy.

A zeroed out memory stick has zillions of bytes of information. I mean thermal entropy.

From the above information we can calculate the temperature of the stick.

I mean the stick is made of thermal energy. Because the stick obeys the law that says that the stick can not be converted to entropyless energy. And all other laws of thermodynamics.

Now when we write some information to the stick we increase its entropy by one zillionth.

So informational entropy itself is physically stored in a way that would equate to the thermodynamical entropy extracted.

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