  In emissions trading, the initial allocation of permits is an intractable
issue because it needs to be essentially fair to the participating countries.
There are many ways to distribute a given total amount of emissions permits
among countries, but the existing distribution methods, such as auctioning and
grandfathering, have been debated. In this paper we describe a new method for
allocating permits in emissions trading using the Boltzmann distribution. We
introduce the Boltzmann distribution to permit allocation by combining it with
concepts in emissions trading. We then demonstrate through empirical data
analysis how emissions permits can be allocated in practice among participating
countries. The new allocation method using the Boltzmann distribution describes
the most probable, natural, and unbiased distribution of emissions permits
among multiple countries. Simple and versatile, this new method holds potential
for many economic and environmental applications.
