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Final Answers
© 2000-2016   Gérard P. Michon, Ph.D.

Demons of Classical Physics

 1749-1827  Lord Kelvin 
 1824-1907  James Clerk Maxwell 
 1831-1879 Rien n'est plus dangereux qu'une idée,
quand on en a qu'une
Alain (Emile Auguste Chartier)  (1868-1951)
Un nouveau dieu  (1930-07-20)
We can't solve problems by using the same kind 
of thinking we used when we created them.

Albert Einstein  (1879-1955)

Related articles on this site:

Related Links (Outside this Site)

Laplace's Demon  by  Linda Garrette.
What is a Maxwellian Demon

The Demons of Classical Physics

These demons were not meant to be evil, but they do haunt physicists.

 1749-1827 (2005-02-18)   Determinism:  Laplace's Demon
Deducing past and future from a detailed snapshot.

[For an intellect knowing  all  positions and velocities]
nothing could be uncertain and the future,
just like the past, would be present before its eyes.

Pierre Simon de Laplace  (1749-1827)

The "intellect" so introduced by the Marquis de Laplace (Essai philosophique sur les probabilités, 1814) has since been dubbed  Laplace's Demon.  It is an icon of the concept of determinism, which can be traced back to Socrates and which was fully entangled with Science before the dawn of  Quantum Theory.  Interestingly, Laplace himself first discussed this in a treatise about probabilities, which deal with the very uncertainty his  Demon  would never have to face.

In fact, Laplace's Demon cannot possibly exist, within this world or outside of it.

From a philosophical or religious standpoint, its existence would preclude free will, which is the one thing that makes the Creation qualitatively different from a lowly clockwork toy.  To be the greatest of creators, it would seem that God had to allow His creation some life of its own, that could escape even Him.  Thus, He did make a stone so heavy that He couldn't lift it:  The quantum Universe.

From a scientific standpoint, even the theoretical possibility of Laplace's Demon condradicts our best understanding of fundamental observations.  In particular, quantum logic is incompatible with so-called hidden variables, which would make Quantum Theory deterministic and allow the entire past and future of the Universe to stand "before the eyes" of the Demon.

Actually, what is ruled out by observation is only the existence of local hidden variables, since this would preclude the violations of Bell's inequality  (John Bell, 1964)  that have been confirmed experimentally.  A priori, some set of nonlocal hidden variables could exist which would make the whole Universe knowable at once.  However, if time can't be separated from the other dimensions  (motion of the observer trades space for time)  we may push the argument of nonlocality to its ultimate conclusion and state that the entire knowledge of the past and future of the Universe would require no part of its history to be unknown, to begin with.

Although a formal proof has yet to be devised, we thus believe in an unavoidable quantum entanglement of the present with a distant past and a distant future.  However, this quantum entanglement is of such a nature that it cannot be used to convey any kind of information.  Information cannot travel faster than light, nor can it go back and forth in time.  Some "time travel" is unavoidable in a relativistic quantum world, but time travelers can't possibly carry any information luggage with them.  Similarly, perpetual motion is mandated by quantum laws, but this motion can't be harnessed to produce useful work for free.

So, there may be a God who knows everything that ever was and ever will be, but there's no such thing as an entity capable of deducing such knowledge from anything but prior knowledge of the same.  Laplace's Demon is a fallacy.

Absolute prior knowledge is next to impossible to fathom in a quantum world...  Could this manifest itself as an  absolute will  transcending  free will  without being incompatible with it?  It just seems easier to believe that the very God who created the quantum  stage  would simply allow the actors to improvise in a loosely scripted play, with a miracle now and then for good measure.

Why can't we remember the Future?

 James Clerk Maxwell 
 1831-1879 (2005-02-18)   Maxwell's Demon   /   Maxwellian Demon
How information is physically traded for entropy.

In a letter that he wrote in December 1867 to his friend Peter Guthrie Tait, the physicist James Clerk Maxwell (1831-1879) described how the action of a "being" controlling a shutter on a  microscopic  hole between two gas containers (A and B) could apparently violate the second law of thermodynamics.

 Lord Kelvin 
 1824-1907 Lord Kelvin ( William Thomson, 1824-1907) is responsible for the name now universally given to this tiny creature:  Maxwell's Demon.

Maxwell's Demon  "looks" at the gas molecules heading toward the hole.  He leaves the hole open only for fast molecules traveling from A to B and slow molecules traveling from B to A.  In Maxwell's own words:  "He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics."

Smoluchowski's Valve  is another version of a  Maxwellian Demon  which raises the pressure of B instead, by letting through only those molecules which travel from A to B.  This was proposed in 1912 by  Marian von Smoluchowski, who also explained why his version of the demon could  not  be physically realized as a tiny door with a weak spring:  The door would soon bounce randomly and become useless.  In fact, we simply can't ignore the temperature and/or entropy of  whatever  is responsible for controlling the hole...

The "contradiction" stated by Maxwel disappears if the second law is carefully stated to account for what the Demon is required to do, which is to physically deal with information about individual molecules.  The resolution of this paradox has helped define the concept of entropy in terms of information.

Instrumental in this analysis was a streamlined version of Maxwell's demon,  which was first considered by Leo Szilard in 1929.  We discuss it below.

Louis Vlemincq  (Belgium.  2005-06-02; e-mail)   Perfect Diode 
Wouldn't a perfect diode produce usable power from thermal electrons?

A device which would allow electrons to flow in only one direction along a wire would, indeed, let thermal electrons gather on one side of it.  This build-up would create a difference in electric potential that could be used to drive a load.  Thus, you'd have a generator whose energy would be ultimately derived from the heat of a single source, in direct violation of the second law of thermodynamics.

Such a device, of course, cannot possibly exist.  It would be to electric potential what Smoluchowski's valve is to pressure.  Both devices seem to work, until one realizes that they will eventually operate at the same temperature as the microscopic entities they are supposed to  control  (electrons in one case, gas molecules in the other).  This makes them completely ineffective at equilibrium.

The characteristic of an actual diode (i.e., the current  I  through it, as a function of the voltage  V  across it)  is always something like the following expression, known as  Shockley's Ideal Diode Equation.  It involves the absolute temperature  T  in a way that prevents violation of the  Second Law.

I   =   Is  [ exp ( qV/nkT ) - 1 ]

  • k = Boltzmann's constant  (in J/K)
  • T = thermodynamic temperature  (in K)
  • q = charge of the electron  (in coulombs)
  • n = emission coefficient  (typically between 1 and 2)
  • Is = saturation current  (proportional to the diode's cross-section)

kT/q  is called the  thermal voltage.  It's equal to  25.6926 mV  at  25°C  and increases at a constant rate  k/q = 86.17343 mV/K  (it's very nearly equal to  25.00 mV  at  17°C  and  30.00 mV  at  75°C).


(2005-05-24)   Szilard's Engine and Landauer's Principle 
At temperature T, an energy   k T ln(2)   is required to erase a bit.

In 1929, Leo Szilard (1898-1964) considered an idealized engine which converts elementary knowledge [one bit of information] into actual work.  The device is immersed in a  single  heat source at temperature T.  It consists of a single gas molecule in a box, with pistons at both ends and a shutter in the middle.

 Szilard's engine

A cycle of Szilard's engine consists of the following steps:

  • The shutter is closed.
  • The demon finds out  which half  of the box the molecule is in.
  • The demon moves the piston in the empty half to the middle of the box.
  • A mechanical load is attached to that piston and the shutter is opened.
  • The molecule pushes the piston back in place, doing  isothermal  work.
  • A new cycle starts, by closing the shutter.

So far so good, it seems we have achieved a "fair" trade between information and mechanical work.  Let's try one obvious way to cheat and bybass the need for the demon's monitoring of information, using the version of Szilard's engine pictured below.  It is identical to the above, except the right piston is fixed and the "usable" work is thus always retrieved at the end of the left piston.

 open  Szilard's engine with one 
 fixed piston an a moving cylinder.  closed

A knowledgeable demon would push (at no cost in energy) either the container or the left piston depending on which half of the container the molecule is in.  We may get the impression that a "dumb" device (like a flywheel) could do just the same, by pushing the left piston when the valve is closed and receiving work when it's open.  Mere synchronization of the valve and the flywheel would seem enough to obtain monothermal work from ambient heat without any counterpart in information.  However, a flywheel connected to the left piston sometimes works directly against the one-molecule gas pressure and/or creates thermal motion of the container between its pistons.  The latter spoils a long-term "blind" synchronization between the flywheel and the valve.  The second law prevails.

The Thermodynamic Cost of Forgetting :

In 1961, Rolf Landauer (1927-1999) put forth what is now known as the "erasure limit", the minimal amount of energy that must be dissipated to erase a given amount of information at temperature T.

Since 1973, Charles H. Bennett (b. 1943) has been investigating computing procedures that do not throw away  any  previously acquired information and thus entail arbitrarily little energy dissipation.  In 1982, Bennett proposed that the Maxwellian demon's inability to break the second law of thermodynamics came from the cost of erasing information, rather than acquiring it.

 Come back later, we're
 still working on this one...

Wikipedia :   Entropy in thermodynamics and information theory

(2005-02-19)   The Power of Knowledge 
Laplace's Demon  and  Maxwell's Demon  are related.

 Come back later, we're
 still working on this one...

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