Computational Information Density and Entropy of the Bitcoin blockchain

Abstract

In econophysics, statistical-physics techniques are used to model economical systems. In this thesis, we investigate the entropy and the Computational Information Density (CID) of the Bitcoin blockchain. The CID is defined as the compression ratio of some particular algorithm when applied to the raw data of the state of the system. It is related to entropy as both CID and entropy are measures of information. We find a strong correspondence between the CID and entropy for the Bitcoin blockchain, where features are similar, but without one being a clear function of the other. This can be explained by intercorrelations between one agent and the next, which the entropy does not count. We also calculate some correlations to see if the CID and the entropy have some predictive power for the price, and we find a small correlation, but very small in comparison to the predictive power of the price itself. These results the power of the CID-entropy correspondence and how the Bitcoin blockchain may be used as a useful large-scale toy model for econophysics. We anticipate that these results can be used for a further look into the CID-entropy relation, as the similarities are visible but there is no exact correspondence. Besides this, these results can form a basis for a further look into the predictive power of the CID or the entropy for the price.