In this work we studied memory and irreversible transport phenomena in a non-equilibrium thermodynamical model for genomic transcriptional regulation. Transcriptional regulation possess an extremely complex phenomenology, and it is, of course, of foremost importance in organismal cell development and in the pathogenesis of complex diseases. A better understanding of the way in which these processes occur is mandatory to optimize the construction of gene regulatory networks, but also to connect these networks with multi-scale phenomena (e.g. metabolism, signalling pathways, etc.) under an integrative Systems Biology-like vision. In this paper we analyzed three simple mechanisms of genetic stimulation: an instant pulse, a periodic biochemical signal and a saturation process with sigmoidal kinetics and from these we derived the system's thermodynamical response, in the form of, for example, anomalous transcriptional bursts.