Entropic Geometry and Information Dynamics in Green Cryptocurrency Markets

Cryptocurrencies play a central role in modern financial markets; however, geopolitical tensions and environmental concerns raise critical questions about their stability and informational efficiency. This study distinguishes between green cryptocurrencies (GCs), based on low-energy validation mechanisms, and dirty cryptocurrencies (DCs), which rely on energy-intensive protocols, to examine their behaviour under geopolitical stress. The objective of this paper is to assess how information dynamics, market resilience, and efficiency differ between GCs and DCs during periods of heightened geopolitical uncertainty, with particular focus on the Russia–Ukraine war. Using daily data from 28 April 2019 to 5 October 2023, we employ advanced information-theoretic measures, including mutual information, the rolling local nearest-neighbour entropy estimator (RLNNEE), and approximate entropy. The results show that DCs exhibit stronger information dominance than GCs, with this gap widening during the conflict. In contrast, GCs display lower but more stable mutual information, indicating greater informational resilience. Approximate entropy further reveals a decline in market complexity during the war period. Overall, the findings highlight the relevance of entropy-based tools for evaluating stability and risk in cryptocurrency markets facing geopolitical shocks.