Thermodynamic uncertainty relations for coherently driven open quantum systems

Abstract

In classical Markov jump processes, current fluctuations can only be reduced at the cost of increased dissipation. To explore how quantum effects influence this trade-off, we analyze the uncertainty of steady-state currents in Markovian open quantum systems. We first consider three instructive examples and then systematically minimize the product of uncertainty and entropy production for small open quantum systems. As our main result, we find that the thermodynamic cost of reducing fluctuations can be lowered below the classical bound by coherence. We conjecture that this cost can be made arbitrarily small in quantum systems with sufficiently many degrees of freedom. Our results thereby provide a general guideline for the design of thermal machines in the quantum regime that operate with high thermodynamic precision, meaning low dissipation and small fluctuations around average values.

Precision bound in periodically modulated continuous quantum thermal machines

“…Finally, we note that violation of the TUR bound Eq. ( 45) has been reported in similar models described by phenomenological master equation and in presence of coherent dynamics [39,46,[48][49][50][51]. Consequently, validity of the TUR bound in absence of secular approximation is an interesting open question, which we plan to address in future works.…”

“…This can be expected as due the secular approximation, the diagonal and offdiagonal elements of the system density matrix evolve independently in time which results in a Pauli type master equation with time independent co-efficients for the occupation probabilities. This, along with the local detailed balance condition, results in the condition R ≥ 2 [14,18,50,73]. Unlike the case of sinusoidal modulation, the noise to signal ratio is not the same for hot and cold currents in case of circular modulation, as can be seen from Fig.…”

“…Extensions to the quantum scenario [38][39][40][41][42][43][44][45] are relatively less explored. In fact, additional complexity that arises due to the genuine quantum features, such as quantum coherence [39,[46][47][48][49][50][51][52] can potentially give rise to violation of the original TUR.…”

Thermodynamics of a continuous quantum heat engine: Interplay between population and coherence

“…The quantum TUR is modified by a different bound [30]. In the present three level system, the violation of the standard TUR was shown in [31,32]. Here, we examine how this result is affected by the modification of the dissipator.…”

“…The higher order correlations of heat flows can be calculated by the introduction of the counting field [31,32]. The dissipator is modified as…”