Monday, May 02, 20163:00 PM - 4:00 PMCNLS Conference Room (TA-3, Bldg 1690)|
Extending Landauer's Bound from Bit Erasure to Arbitrary Computation
David WolpertSanta Fe Institute
Recent advances in nonequilibrium statistical physics have led to great strides in the thermodynamics of computation, allowing the calculation of the minimal thermodynamic work required to implement a computation 𝝅 when two conditions hold:
i) The output of 𝝅 is independent of its input (e.g., as in bit erasure);
ii) We use a physical computer C to implement 𝝅 that is tailored to the precise distribution over 𝝅's inputs, P0.
First I extend these analyses to calculate the minimal work required even if the output of 𝝅 depends on its input. I then show that stochastic uncertainty about P0 increases the minimal work required to run the computer.
Next I show that if C will be re-used, then the minimal work to run it depends only on the logical map 𝝅, independent of the physical details of C. This establishes a formal identity between the thermodynamics of (re-usable) computers and theoretical computer science. I use this identity to prove that the minimal work required to compute a bit string 𝝈 on a universal Turing machine U is
log (Bernoulli measure of the set of input strings that compute 𝝈)
log(halting probability of U)
This can be viewed as a thermodynamic “correction” to Kolmogorov complexity.
I end by using these results to relate the free energy flux incident on an organism / robot / biosphere to the maximal amount of computation that the organism / robot / biosphere can do per unit time.
Host: Sebastian Deffner