Thermodynamics of computation and information distance
Applying the tools of algorithmic information theory, we compare several candidates for an asymptotically machine-independent. absolute measure of the informational or cognitive'' distance between discrete objects x and y. The maximum of the conditional Kolmogorov complexities max[l brace]K(y[vert bar]z) K(m[vert bar]y)[r brace], is shown to be optimal, in the sense of being minimal within an additive constant among semicomputable, symmetric, positive semidefinite functions of z and y satisfying a reasonable normalization condition and obeying the triangle intequality. The optimal metric, in turn, differs by at most an additive logarithmic term from the size of the smallest program for a universal reversible computer to transform x into y. This program functions in a 'catalytic'' capacity, being retained in the computer before, during, and after the computation. Similarly, the sum of the conditional complexities. K(y[vert bar]x) + K(x[vert bar]y), is shown to be equal within a logarithmic term to the minimal amount Of information flowing out and in during a reversible computation in which the program is not retained. Finally. using the physical theory of reversible computation, it is shown that the simple difference K(x) - K(y) is an appropriate (ie universal, antisymmetric, and transitive) measure of the amount of thermodynamic work required to transform string x into string y by the most efficient process.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE; USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 6230593
- Report Number(s):
- LA-UR-93-1569; CONF-9306155-1; ON: DE93012730
- Resource Relation:
- Conference: Symposium on theory of computation (STOC), San Diego, CA (United States), 7-11 Jun 1993
- Country of Publication:
- United States
- Language:
- English
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71 CLASSICAL AND QUANTUM MECHANICS
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990200* - Mathematics & Computers
661300 - Other Aspects of Physical Science- (1992-)