CitationsAdd new citationList by: CiterankMap Link[1] Landauer's principle
Author: Wikipedia Cited by: Peter Baldwin 1:15 AM 4 July 2011 GMT URL: | Excerpt / Summary Rationale
Landauer's principle can be understood to be a simple logical consequence of the second law of thermodynamics—which states that the entropy of a closed system cannot decrease—together with the definition of thermodynamic temperature. For, if the number of possible logical states of a computation were to decrease as the computation proceeded forward (logical irreversibility), this would constitute a forbidden decrease of entropy, unless the number of possible physical states corresponding to each logical state were to simultaneously increase by at least a compensating amount, so that the total number of possible physical states was no smaller than originally (total entropy has not decreased). Yet an increase in the number of physical states corresponding to each logical state means that for an observer who is keeping track of the logical state of the system but not the physical state (for example an "observer" consisting of the computer itself), the number of possible physical states has increased; in other words, entropy has increased from the point of view of this observer. The maximum entropy of a bounded physical system is finite. (If the holographic principle is correct, then physical systems with finite surface area have a finite maximum entropy; but regardless of the truth of the holographic principle, quantum field theory dictates that the entropy of systems with finite radius and energy is finite.) So, to avoid reaching this maximum over the course of an extended computation, entropy must eventually be expelled to an outside environment at some given temperature T, requiring that energy E = ST must be emitted into that environment if the amount of added entropy is S. For a computational operation in which 1 bit of logical information is lost, the amount of entropy generated is at least k ln 2, and so the energy that must eventually be emitted to the environment is E ≥ kT ln 2. This expression for the minimum energy dissipation from a logically irreversible binary operation was first suggested by John von Neumann, but it was first rigorously justified (and with important limits to its applicability stated) by Landauer. For this reason, it is sometimes referred to as being simply the Landauer bound or Landauer limit.
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