Impact of Information on Quantum Heat Engines

TL;DR

This work presents a concrete framework for a two-stroke quantum heat engine coupled to multiple baths and Maxwell's demon, treating the engine and the demon's memory as a unified hybrid system. By deriving thermodynamic bounds that couple von Neumann information, Landauer cost, and Clausius relations, it shows how information gathering and processing constrain performance and prevent second-law violations. The study introduces the Landauer efficiency and its maximum form, distinguishes fine-grain from coarse-grain measurements, and demonstrates, through a two-qubit example, that more information does not always optimize performance; in some regimes, coarse-grained measurements yield higher efficiency and even greater work output. These insights inform design principles for nanoscale quantum thermal devices and highlight trade-offs between information gain and energetic cost in quantum feedback control.

Abstract

The emerging field of quantum thermodynamics is beginning to reveal the intriguing role that information can play in quantum thermal engines. Information enters as a resource when considering feedback-controlled thermal machines. While both a general theory of quantum feedback control as well as specific examples of quantum feedback-controlled engines have been presented, still lacking is a general framework for such machines. Here, we present a framework for a generic, two-stroke quantum heat engine interacting with $N$ thermal baths and Maxwell's demon. The demon performs projective measurements on the engine working substance, the outcome of which is recorded in a classical memory, embedded in its own thermal bath. To perform feedback control, the demon enacts unitary operations on the working substance, conditioned on the recorded outcome. By considering the compound machine-memory as a hybrid (classical-quantum) standard thermal machine interacting with $N+1$ thermal baths, our framework puts the working substance and memory on equal footing, thereby enabling a comprehensible resolution to Maxwell's paradox. We illustrate the application of our framework with a two-qubit engine. A remarkable observation is that more information does not necessarily result in better thermodynamic performance: sometimes knowing less is better.

Figures (3)

• Figure 1: Schematic of the physical model for a feedback-controlled quantum heat engine. The multi-partite working substance (WS) of the heat engine, outlined in a dotted black rectangle, is comprised of quantum systems, each in contact with their own thermal bath, possibly at different temperatures, $T_1, ..., T_N$. The extended working substance (xWS), outlined by the solid black rectangle, extends the heat engine to include the demon's memory, which is in thermal contact with yet another thermal bath at temperature $T_0$. The demon measures the WS, writing the result $\alpha$ into memory. Based on the value of $\alpha$, the demon enacts a corresponding unitary $U_{\alpha}$ on the WS.
• Figure 2: Comparison of max-work Landauer efficiency $\eta^L_W$ for fine- and coarse-grain measurement in the $\boldsymbol{E}$ and Bell bases as a function of bath temperature $T_1$ of qubit 1.
• Figure 3: Comparison of total work output $W_{\text{out}}$ and Landauer cost of information gathering $Q_0^L$ for fine- and coarse-grain measurement in the $\boldsymbol{E}$ and Bell bases as a function of bath temperature $T_1$ of qubit 1.