Abstract
We survey a few aspects of the thermodynamics of computation, connecting information, thermodynamics, computability and physics. We suggest some lines of research into how information theory and computational thermodynamics can help us arrive at a better understanding of biological processes. We argue that while a similar connection between information theory and evolutionary biology seems to be growing stronger and stronger, biologists tend to use information simply as a metaphor. While biologists have for the most part been influenced and inspired by information theory as developed by Claude Shannon, we think the introduction of algorithmic complexity into biology will turn out to be a much deeper and more fruitful cross-pollination.
Highlights
Unifying Information and Energy through ComputationWhen Alan Turing defined the concept of universal computation, he showed that any given Turing machine could be encoded as the input of another (universal) Turing machine
We survey a few aspects of the thermodynamics of computation, connecting information, thermodynamics, computability and physics
As Cooper would have it, this amounted to the disembodiment of computation [1], because Turing made clear that even though computation seemed to require a physical carrier, the physical carrier itself could be transformed into information
Summary
When Alan Turing defined the concept of universal computation, he showed that any given Turing machine could be encoded as the input of another (universal) Turing machine. Szilárd showed that if one had one bit of information about a system, one could use that information to extract an amount of energy given by E = (log2 )kT (where k is Boltzmann’s constant, and T the temperature of the system) Landauer studied this thermodynamical argument [3] and proposed a principle: if a physical system performs a logically irreversible classical computation, it must increase the entropy of the environment with an absolute minimum of heat release amounting to E per lost bit. Algorithmic probability (just like algorithmic—Kolmogorov—complexity [13,14]) is non-computable [14,16], which means that one cannot predict an incoming string with complete accuracy, and that there is no way, not even in principle, to extract work from a piston Turing machine if the incoming input is random. No algorithm can predict the bit of an algorithmically random sequence
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