Functions per second produced by a program is relevant to halting theory and the computational complexity of a decision problem. Strings and state function transactions are an important measurement of computer performance.
The conventional computational complexity models describe the resources limitations in terms of time and memory required to process a random string and other data structures. In algorithmic information theory, however, the string complexity is described in terms of the limitations related to the language used to program an arbitrary decision problem and the statistical distribution of input and output strings. In this paper we look for a more fundamental limit: the thermo-computational constraints related to process information.
A Turing Machine instantiation such as a Carnot Engine processing signals is transforming information within a discrete, thermodynamic physical system that has storage regions of high and low entropy. The energy source is converted to string computing effort but is also lost as heat and noise, such observed with thermal and quantum noise.
The energy efficiency of a computation-communication system can be measured in Joule per bits (J/bits) and Bits per second (Bits/s). The proposed general optimization challenge is how can any arbitrary binary program be improved in terms of the energy change rate and final entropy state, computed by a machine with finite energy constrains.
In other words, this can be summarized as “what is the minimal volume of energy change required to describe and compute a bit of information”.
In this work we have applied this concept to optimize the search for the optimal network routing path in a set of distributed and interconnected machines nodes with an arbitrary topology. The results obtained from the experiment provides a better string optimization factor with an average information gain performance of 11.52% versus 8.53% from benchmark. The expected energy difference between the proposed QA and the benchmark SA algorithms is approximately 8.11%. The findings and proposed framework can be expanded to the energy efficiency of other non-polynomial problems.