Boltzmann Entropy in Cryptocurrencies: A Statistical Ensemble Based Approach

In this paper we try to build a statistical ensemble to describe a cryptocurrency-based system, emphasizing an "affinity" between the system of agents trading in these currencies and statistical mechanics. We focus our study on the concept of entropy in the sense of Boltzmann and we try to extend such a definition to a model in which the particles are replaced by N agents completely described by their ability to buy and to sell a certain quantity of cryptocurrencies. After providing some numerical examples, we show that entropy can be used as an indicator to forecast the price trend of cryptocurrencies.