Quantitative comparison of different time-periodic Thermodynamic Uncertainty Relations

Thermodynamic Uncertainty Relations (TUR) comprise a general bound for fluxes in nonequilibrium processes [1], they represent a trade-off between signal and noise for steady state thermodynamic fluxes (e.g. particle flow, heat delivered to a thermal reservoir, substrate molecules consumption) in Markov processes. These quantities fluctuate and the TURs relate their average and variance to the entropy production of the process, which is a measure of irreversibility and therefore the relation can also be rearranged to bound the efficiency of mesoscopic engines.

These relations have been verified in a number of theoretical and experimental works, however there is a lack of quantitative discussion about how tight different TURs can be, which is a very important question since they can be used to infer entropy production. In this talk I will show results for an exactly solvable model and how 4 different TURs behave in the periodic steady state to characterize how tight they are and if there is one that stands out among them [2].

[1] Horowitz, Jordan M., and Todd R. Gingrich. Nature Physics 16.1 (2020): 15-20
[2] Harunari, Pedro E., Carlos E. Fiore, and Karel Proesmans. Journal of Physics A: Mathematical and Theoretical 53.37 (2020): 374001