Saeid Tahmasebi

Extropy is a concept that represents the potential for improvement, growth, and positive advancement within systems, particularly in the realms of human society, technology, and consciousness. It is often seen as the counterpart to entropy, which is associated with disorder and decline. While entropy quanties the tendency of systems to move toward disorder over time, extropy embodies the idea of increasing order, complexity, and intelligence. The term is frequently used in discussions around transhumanism and futurism, where it highlights the pursuit of progress, enhancement, and the expansion of human capabilities through technological and innovative means. Extropy advocates for a proactive approach to shaping the future, leveraging knowledge and technology to create a more advanced and improved world. In essence, extropy can be understood as a measure of the potential for positive change, growth, and the enhancement of life, serving as a guiding principle for those striving to optimize human existence and societal structures. While entropy and extropy are related, they are distinct concepts-essentially two sides of the same coin. In this paper, we introduce the concept of extropy in the context of uncertain random variables. We derive a formula for calculating the extropy of uncertain random variables using inverse uncertainty distributions. Additionally, by interpreting extropy as a measure of order, we apply it to optimize portfolio selection problems using mean-variance-extropy models .