Stochastic Thermodynamics: cost of precise biochemical oscillations and active heat engines

I will provide a brief introduction to stochastic thermodynamics, a modern theoretical framework that generalizes thermodynamics to small nonequilibrium systems. Two prominent relations in the field will be discussed. The older fluctuation theorem and the more recent thermodynamic uncertainty relation that we obtained in 2015. I will then talk about two of our recent results. First, for biochemical oscillations, such as circadian rhythms, in stochastic systems, we have conjectured the universal minimal free energy cost of coherent oscillations. Second, active cyclic heat engines are heat engines with a working substance is in the presence of hidden dissipative degrees of freedom such as bacteria. In this case, the external bath is an active medium (or active matter). We have derived a generic second law for active heat engines, which has been a challenge since active heat engines have been introduced in an experiment in 2016.