From Physics to Environmental Policy: Exploring Boltzmann Distribution for Carbon Trading Permit Allocation

Combating climate change and reducing atmospheric CO2 emissions are imperative. While carbon trade, including taxes and trading systems, has been proposed, the allocation of initial permits is challenging. This study addresses this issue, exploring the application of the Boltzmann distribution for carbon emission permit allocation in carbon trading. The Boltzmann distribution method uniquely considers each country's environmental and economic contexts, assigning more responsibility to nations with larger populations and higher emissions, and providing incentives to lower-emission countries. This promotes fairness in global climate change efforts and influences national environmental policies. High-emission countries like China receive a high number of permits, encouraging stronger environmental policies, whereas countries with lower emissions, such as Italy, benefit from additional permits as compared to conventional distribution models, bolstering their existing environmental conservation. This paper applies the Boltzmann distribution to eight countries, considering population, economic size, and CO2 emissions. It effectively balances permits between egalitarianism (population-based) and sovereignty (emission-based) principles, suitable for international carbon trading. This flexible approach provides a practical framework for international emissions rights allocation along with potential applications in broader contexts. Implementation of the Boltzmann distribution in real-world policy faces challenges due to the dynamic nature of international politics and economics. This research offers insights into the process of integrating this method into existing environmental policy frameworks, demonstrating its potential as a tool for enhancing global environmental sustainability. Future research should explore its application in the complex international political and economic environment, furthering its role in global climate policy.