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This study examines the dynamic causality between the carbon emission market and the clean energy market, using an information flow-based, quantitative Liang causality analysis which is firmly grounded on physics and derived from first principles. The dynamic causal relationships between European Union Allowance (EUA) prices and clean energy index allow us to explore whether the causality in return or in variance from CO2 emission allowances to the clean energy index is time-varying. The results show that the causal relationships in return and in variance between EUA and Clean Energy Index (CEI) are drastically time-varying. For the causality in return, a significant unidirectional long-term and stable causality from CEI to EUA is identified after March 2020. For that in variance, a bidirectional causality is found after March 2020, but values after 2020 are opposite to those in return. It seems when fluctuations in the clean energy market are low, the clean energy market has a weak causal effect on the carbon emission market but when volatility in the clean energy market is increasing, causalities between the two markets are significantly strengthened. These results obtained through this rigorous causality analysis can serve as a reference for academics, market participants, and policymakers to understand the underlying links between EUA prices and clean energy index. [ABSTRACT FROM AUTHOR]