Precision-dissipation trade-off for driven stochastic systems

Over the last few decades, stochastic thermodynamics has emerged as a framework to study the thermodynamics of small-scaled systems. The relation between entropy production and precision is one of the most prominent research topics in this field. In this paper, I answer the question how much dissipation is needed to follow a pre-determined trajectory. This will be done by deriving a trade-off relation between how precisely a mesoscopic system can follow a pre-defined trajectory and how much the system dissipates. In the high-precision limit, the minimal amount of dissipation is inversely proportional to the expected deviation from the pre-defined trajectory. Furthermore, I will derive the protocol that maximizes the precision for a given amount of dissipation. The optimal time-dependent force field is a conservative energy landscape which combines a shifted version of the initial energy landscape and a quadratic energy landscape. The associated time-dependent probability distribution conserves its shape throughout the optimal protocol. Potential applications are discussed in the context of bit erasure and electronic circuits.