Tightening the thermodynamic uncertainty relations with null-entropy events: What we learn when nothing happens

Fluctuation theorems establish that thermodynamic processes at the microscale can occasionally result in negative entropy production. At such scales, another distinct possibility becomes more likely: processes in which no entropy is produced overall. In this work, we explore the constraints imposed by such null-entropy events on the fluctuations of thermodynamic currents. By incorporating the probability of null-entropy events, we obtain tighter bounds on finite-time thermodynamic uncertainty relations derived from fluctuation theorems. Our results are directly applicable to both quantum and classical systems that satisfy the fluctuation theorem. We validate our framework using an example of a qudit SWAP engine.