Thermodynamic uncertainty relations for relativistic quantum thermal machines

TL;DR

The paper investigates how relativistic motion of Unruh–DeWitt detectors as the working medium in a two-qubit SWAP entropy machine affects fluctuation relations and performance. By deriving the cumulant generating function for work and heat, it establishes thermodynamic uncertainty relations that can be violated due to quantum and relativistic effects, and it formulates generalized bounds on efficiency and COP using effective temperatures. The results show that relativistic motion can enhance engine and refrigerator performance and even surpass standard Carnot limits based on rest-frame temperatures, revealing a rich interplay between relativity and nonequilibrium quantum thermodynamics. These insights have potential implications for designing quantum thermal devices operating in relativistic or high-velocity regimes and for understanding fundamental limits of quantum thermodynamics in moving frames.

Abstract

We investigate a two-qubit SWAP thermal machine -- a streamlined analogue of the four-stroke Otto cycle -- whose working medium comprises inertially moving Unruh-DeWitt qubit detectors, each coupled to a thermal quantum field bath prepared at a different temperature. In the presence of relative motion between the working medium and the thermal baths, we derive thermodynamic uncertainty relations (TURs) that quantify the trade-off between performance, entropy production, and power fluctuations. Our analysis identifies regimes where relativistic motion leads to stronger violation of classical TURs, previously observed in static quantum setups. In addition, we establish generalized performance bounds for the thermal machine operating as either a heat engine or a refrigerator, and discuss how relativistic motion can enhance their performances beyond the standard Carnot limits defined by rest-frame temperatures.

Figures (3)

• Figure 1: Heat variance, $\text{Var}(Q_H)$, as a function of the transition frequency ration $\omega_B/\omega_A$, compared with the bound \ref{['bound:analytic']}, the standard TUR \ref{['TUR']}, and the generalized bound \ref{['TUR:gen']}. The temperature ratio between the thermal baths is fixed at $\beta_A/\beta_B = 1/2$. (a) Qubit B moves through the cold bath with speed $\upsilon_A=0.8$. (b) Qubit A moves through the hot bath with speed $\upsilon_A=0.8$. The vertical lines indicate the boundary between the different regimes of operation of the machine.
• Figure 2: The ratio $\mathcal{R}$ for different qubit velocities as a function of $\omega_B\beta_B$ with $\omega_A\beta_A=0.5$, and as a function of $\omega_A\beta_A$ with $\omega_B\beta_B=0.5$. The black dotted line corresponds to the static case $\upsilon_A\!=\!\upsilon_B\!=\!0$. Values below 2 indicate that the bound is looser than the standard TUR.
• Figure 3: Left panel: Cooling power, $\expval{Q_C}$, as a function of the frequency ratio $\omega_B/\omega_A$, for a fixed temperature ratio of the thermal baths $\beta_A/\beta_B = 1/2$ and varying qubit speeds. The black dotted line corresponds to the static case $\upsilon_A\!=\!\upsilon_B\!=\!0$. The vertical line indicates the boundary between refrigerator and heat engine operational regimes in the rest-frame case. Right panel: COP at maximum figure of merit, $\varepsilon^*$, as a function of the velocity of the qubit $A$, when $\beta_A/\beta_B = 0.65$. Here, $\varepsilon_C$ is the standard Carnot COP, and $\varepsilon_C^{\text{eff}}$ the generalized Carnot bound.