Information flow dynamics between cryptocurrency returns and electricity consumption: A comparative analysis of Bitcoin and Ethereum

•Comparative analysis of Bitcoin and Ethereum electricity consumption and returns.•Ethereum's transition to PoS shows a stronger link between returns and energy use.•Shannon and Rényi transfer entropy reveal bidirectional information flow dynamics.•Ethereum returns significantly impact energy consumption, unlike Bitcoin.•A dynamic approach captures time-varying effects of market changes on energy use. Understanding energy consumption associated with cryptocurrency mining gained increasing attention, with the literature focusing mainly on Bitcoin. This study uses data from the two energy consumption indices, to estimate static and dynamic transfer entropies. The results provide a nuanced understanding of the bidirectional relationships and their implications. The dominant direction of information flow for Bitcoin is from electricity consumption to returns, while for Ethereum, it is from returns to electricity consumption, suggesting that Ethereum's returns significantly impact electricity consumption patterns. Results highlight the need for policies that integrate energy forecasting and environmental sustainability considerations and has significant implications for policymaking.