Thursday, November 13, 2014

wikipedia maxwell's demon edit

In previous discussion "meaning of life" I tried to speculate that maybe a replicator could makes copies from internal energy without waste, and therefore the copies would indicate a decrease in entropy at the expense of kinetic and potential energy.  Every scientist should know this is impossible from the 2nd law of thermodynamics.  Here is my post on "Maxwell's demon" to describe in the most immediate and clear sense possible of why breaking the 2nd law is impossible, without having to use quantum mechanics to derive entropy....i.e. without having to resort to good understanding of entropy.
In his 1962 lectures physicist Richard Feynman analyzed a tiny paddlewheel attached to a ratchet, explaining why it cannot extract energy from molecular motion of a fluid at equilibrium.[18] He explained how this device is equivalent to what he called the simplest Maxwell's demon, Smoluchowski's trap door (Vol I, 46-3).
The ratchet is superficially different from the demon by trying to generate work W as opposed to creating a heat differential that has an entropy decrease dS. The dS could supply the W (and vice versa) if both systems had perfect efficiency, i.e. W=dQ=T*dS. Stated another way, a working ratchet can be used to create a heat differential by extracting energy from a weight being lowered instead of attempting to raise it.[19]
The devices attempt to violate the second law of thermodynamics from the kinetic energies of randomly-distributed molecules at an ambient temperature. A weak chemical bond that holds either the pawl or arbitrarily small trap door in place has to be strong enough to prevent thermal motions from breaking the bond. They must be thermally connected to the gas or fluid because they must have a physical (thermal) path for a force to prevent reverse operation. The door and pawl bonds correspond to a memory "bit" that registers if the pawl or door are in an open state. They fail because the attempted gain in energy from the ratchet and the attempted decrease in entropy from the demon require a quick reconnection of that bond, which is the erasure of a memory bit that is shown by Landauer's Principle to be a loss in energy of at least k*T*ln(2), creating an increase in entropy of at least k*ln(2) at that operating temperature. This minimal bit has less information content than a Shannon bit which has an entropy of log2(2) because it contains the maximum amount of thermal noise, keeping its memory state less reliably than the bond of a van der Waals force, barely maintaining a 50% probability of being in the correct state at any given moment. If the memory bit (as physically implemented as a pawl or trap door) is made more reliable by a stronger chemical bond, the length of time necessary to wait for a sufficiently energetic occurrence to compensate for the increase in heat generated in the bit erasure step (reconnection) will exactly offset the increased reliability.
Modern considerations of the demon ignore the observation step or merge it with his memory.[20] The ratchet does not utilize an observer separate from the "memory" of the pawl's position, unless the paddlewheel is considered the "observer". Similarly, the demon's door is considered an arbitrarily small "observer", using a portion of the higher-than-average-velocity molecule's energy to open, as does the pawl.
After the ratchet's pawl or the demon's door are "activated", they must reset very quickly before the gain in energy or decrease in entropy is lost. Opening the bond requires either external energy or energy that was stored in the system, such as kinetic energy form the higher-than-average-energy molecule that is approaching. The breaking of the bond has to add (or transfer) kinetic energy to the moving pawl or door in order for it remain at equal temperature to the surroundings. This is not the exothermic or endothermic nature of the bond which will balance out in each cycle, but more precisely its exergonic and endergonic nature which includes temperature and entropy instead of just enthalpy. But we want to subtract out the enthalpy because it cancels in each cycle, which means we just want to consider the necessary kinetic energy added to and subtracted from the moving part as it has gained at least one degree of freedom of movement. The reconnection of the moving part releases that extra kinetic energy as additional heat to the system, making the pawl and latch more likely to be open when they should not be. This resetting is the erasure of the memory "bit" of the pawl or door being in the "on" position.
These are Carnot-cycle type devices that do not utilize a large or infinite number of pawls and latches (i.e., a large "memory bank") designed to be used only once and therefore not resetting (i.e. no memory erasure, therefore no exergonic reaction). However, a "memory bank" design would need to start in a more organized manner with either more potential energy or less entropy at the start of its operation than at the end, equivalent to the gains attempted.

No comments:

Post a Comment