Thermodynamic Uncertainty Relation for Charge Transport – Multilevel Setup

Abstract

The tremendous advances in technology achieved over the past few decades have made possible engineering thermoelectric devices at astonishingly small scales, scales at which we can no longer neglect the inherent fluctuations. Recently, it was shown that the fluctuations in small-scale systems are constrained by the entropy production of the nonequilibrium process through the Thermodynamic Uncertainty Relation (TUR). This relation translates to a trade-off between the precision of the output and the thermodynamic cost of producing it. In this thesis, we study the TUR in the context of the resonant charge transport model. We show that this ratio goes beyond the classical limit for our system both in the strong and weak coupling regimes. We also study the influence of quantum coherences on this ratio. In particular, we discover that the TUR saturates with system size for quantum dots with sequential tunneling and achieves the lower bound 1.246 for $N \geq 3$, which is the main result of this work. We explain the saturation of the TUR bound by similar behaviour of the mean current and current fluction integrals. We also present new bounds on TUR-like ratios involving higher-order cumulants through numerical simulations. Our results thereby provide significant insights into the important and relevant goal of achieving high thermodynamic precision - small fluctuations at a low dissipative cost.