Buckle up and prepare for an interdisciplinary rollercoaster of a nutshell seminar. It will feature a physicist trying to explain some biology to mathematicians. Thermodynamics considers life as an open out-of-equilibrium system that exchanges energy and matter with its environment. Through conversions these can be exploited by the cell to maintain its internal processes and grow. During these processes, energy is dissipated which produces entropy. Earlier results suggest that entropy production rate (EPR) is an important quantity for microbial growth. From biophysical intuition one could expect that EPR always increases with growth rate. We show that this is true for microorganisms cultivated in a chemostat with a fixed conversion of substrates into products. Some microbes however show a metabolic shift as function of their growth rate, which changes their net conversion. This may result in a reduced EPR at increasing growth rate. We analyze this situation using chemostat models of yeast, which we parameterized with experimental data. We also derive a quantitative criterion that can be used to predict the EPR of shifts in metabolic strategies across microbial species. If time permits, we will also dive into the intracellular metabolic processes and the corresponding thermodynamics and discuss future ideas to model this.