Spontaneous Chiral Symmetry Breaking and Entropy Production in a Closed System

In this short article, we present a study of theoretical model of a photochemically driven, closed chemical system in which spontaneous chiral symmetry breaking occurs. By making all the steps in the reaction elementary reaction steps, we obtained the rate of entropy production in the system and studied its behavior below and above the transition point. Our results show that the transition is similar to a second-order phase transition with rate of entropy production taking the place of entropy and the radiation intensity taking the place of the critical parameter: the steady-state entropy production, when plotted against the incident radiation intensity, has a change in its slope at the critical point. Above the critical intensity, the slope decreases, showing that asymmetric states have lower entropy than the symmetric state.

Minimally doubled fermions and spontaneous chiral symmetry breaking

Chiral symmetry breaking in massless QCD is a very important feature in the current understanding of low energy physics. Low - lying Dirac modes are suitable to help us understand the spontaneous chiral symmetry breaking, since the formation of a non zero chiral condensate is an effect of their accumulation near zero. The Banks – Casher relation links the spectral density of the Dirac operator to the condensate with an identity that can be read in both directions. In this work we propose a spectral method to achieve a reliable determination of the density of eigenvalues of Dirac operator near zero using the Gauss – Lanczos quadrature. In order to understand better the dynamical chiral symmetry breaking and use the method we propose, we have chosen to work with minimally doubled fermions. These kind of fermions have been proposed as a strictly local discretization of the QCD fermions action, which preserves chiral symmetry at finite cut-off. Being chiral fermions, is easier to work with them and their low - lying Dirac modes and to understand the dynamical spontaneous chiral symmetry breaking.