Entropy of the quantum fluctuations of fermionic instantons in the universe

Abstract

The aim of this paper is to study the entropy of quantum fluctuations of fermionic instantons. For this purpose, we focus on the spinor-type instanton solution family of the massless pure fermionic Thirring model because it is a well-known quantized toy model in the quantum field theory since 1958. We calculate the Boltzmann-Gibbs-Shannon (BGS) entropy of the Thirring model by the normalized inner scalogram (NIS) and find that the entropy of quantum fluctuations of Thirring fermionic instantons increase slightly just after the big bang. This result leads us to discuss the relation between the increasing entropy in the Universe due to quantum fluctuations of the fermionic Thirring instantons during the creation of fermionic type particles.