In this presentation it will be shown that there is a possibility to establish direct connections between some applications of statistical mechanics and analysis of algorithmic processing. As a basis we assume that a computer system is a machine in which we have a transformation of free energy into useful work, i.e., mathematical computations. We present the case of quick-sort algorithm and its statistical mechanics analysis in terms of possible existence of long-range dependencies. Sorting is one of the most frequently used types of processing in computer systems. In our approach sorting will be considered as an introduction of order into processed input task and algorithm as a physical system. Our analysis will show how the dependencies in processed tasks can influence the behavior of algorithm (or equivalently Turing machine). Normally, analysis of any algorithm behavior is done in terms of classical computational complexity, which usually considers only tree cases: pessimistic, optimistic and average assuming that only those instances are important. This is done in order to ensure the independence of this measure on specific input sets properties. However, this approach doesn’t allow to answer some interesting questions, for example: is there any influence of input set on processing dynamics? In the case of quick sorting this question will be: is there any influence of input set properties (for example the existence long-range dependencies) on quick sorting dynamics. In our research we show that such a dependency exists. The investigations are based on computer simulations performed for set of 1000 instances with different values of H parameter. Each input set has 10⁶ elements. The rate of existence of long-term correlations in processing dynamics is calculated basing on Hurst coefficient. This allows for description of this algorithm in a different way: as a physical machine in which processing (energy consumption) is governed or not by long-range dependencies.

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