Precision of an autonomous demon exploiting nonthermal resources and information

TL;DR

This work investigates a three-quantum-dot refrigerator that exploits a nonthermal resource to achieve cooling with zero average energy exchange from the resource. Using full counting statistics and stochastic trajectories in the sequential-tunneling regime, the authors quantify cooling power, fluctuations, and information flow, contrasting two operating principles: an information-based Maxwell-demon-like mode and a nonthermal-resource-based mode. They show that the nonthermal regime can suppress cooling-power fluctuations relative to input fluctuations by up to an order of magnitude, while the information-based regime remains noisier; cross-correlations between heat and information currents reveal the distinct working mechanisms. The findings highlight how multi-terminal nanoscale engines can achieve high-precision cooling without large average energy transfer and suggest design principles for minimizing noise in thermodynamic tasks at the quantum scale.

Abstract

Quantum-dot systems serve as nanoscale heat engines exploiting thermal fluctuations to perform a useful task. Here, we investigate a multi-terminal triple-dot system, operating as a refrigerator that extracts heat from a cold electronic contact. In contrast to standard heat engines, this system exploits a nonthermal resource. This has the intriguing consequence that cooling can occur without extracting energy from the resource on average -- a seemingly demonic action -- while, however, requiring the resource to fluctuate. Using full counting statistics and stochastic trajectories, we analyze the performance of the device in terms of the cooling-power precision, employing performance quantifiers motivated by the thermodynamic and kinetic uncertainty relations. We focus on two regimes with large output power, which are based on two operational principles: exploiting information on one hand and the nonthermal properties of the resource on the other. We show that these regimes significantly differ in precision. In particular, the regime exploiting the nonthermal properties of the resource can have cooling-power fluctuations that are suppressed with respect to the input fluctuations by an order of magnitude. We also substantiate the interpretation of the two different working principles by analyzing cross-correlations between input and output heat currents and information flow.

Figures (15)

• Figure 1: (a) A resource region formed by two capacitively coupled quantum dots---each connected to one electronic reservoir, H or C---acts on a single quantum dot, W---connected to two reservoirs L and R---forming the working substance. A particle current $J^N$ can thereby be induced between contacts R and L, while heat currents $J_\alpha^Q$ flow out of (or into) each of the four reservoirs. The system works as a refrigerator when ${\cal P}_{\rm cool}=J^Q_\text{R}>0$. (b) The reservoirs are kept at electrochemical potential $\mu_\alpha$ and temperature $T_\alpha$. Electrons tunnel from/to the reservoirs into/from the single level at energy $\epsilon_\text{W}+hU_\text{H}+cU_\text{C}$ in dot W or $\epsilon_j+wU_j$ in dots $j=$ H,C, where $h$, $c$ and $w$ are the occupations of dots H, C and W. Tunneling rates $\Gamma_\text{H}$ and $\Gamma_\text{C}$ are energy independent, while the tunneling rates, $\Gamma_\alpha^{hc}$ for dot W are energy dependent. We consider the ideal case where $\Gamma_\alpha^{hc}$ vanishes either when $h=c=0$ and $\alpha= \text{R}$, or when either $h=1$ or $c=1$ and $\alpha=\text{L}$ (as indicated by the red crosses).
• Figure 2: (a) Cooling power maximized over $\epsilon_\text{C}$ and $\epsilon_\text{W}$, $\mathcal{P}_\text{cool}^{\epsilon \text{max}}$ (solid orange line), and the corresponding fluctuations in the cooling power, ${S}_{\mathcal{P}_\text{cool}\mathcal{P}_\text{cool}}$, (dashed blue line) as functions of $U_\text{H}$ (reproducing the results from Ref. InfoTrajPaper). (b) TUR and KUR performance quantifiers, as defined in Eqs. \ref{['Q_TUR']}, \ref{['Q_KUR']}, and \ref{['Q_KUR_loc']}, when optimizing for cooling power. (c) Ratio of the cooling-power noise and input-current noise when optimizing for cooling power. The vertical dotted black lines indicate two specific parameter sets which will be called scenarios (I) and (II), see also Table \ref{['tab:params']}. Parameters (in units of $\Gamma_\text{C} =\Gamma_\text{H} =\Gamma$): $T_\mathrm{H} = 16$, $T_\mathrm{C} = 4$, $\bar{T} = 8$, $\delta T = 1$, $U_\text{C}=12$, $\Gamma_\text{R}^{00} = \Gamma_\text{L}^{01} = \Gamma_\text{L}^{10} = 0$ and $\Gamma_\text{L}^{00} = \Gamma_\text{R}^{01} = \Gamma_\text{R}^{10} = 0.01$.
• Figure 3: (a) Average cooling power $\mathcal{P}_\text{cool}$ and (b) cooling power noise ${S}_{\mathcal{P}_\text{cool}\mathcal{P}_\text{cool}}$ as functions of $\epsilon_\text{W}$ and $\delta T = T_\mathrm{L} - T_\mathrm{R}$. We choose the value of $\epsilon_\text{C}$ maximizing $\mathcal{P}_\text{cool}$ for each $\epsilon_\text{W}$ and $\delta T$, while $\epsilon_\text{H}$ is always taken such that $J^Q_\text{in} = 0$. The parameters have the values of scenarios (I) and (II) (as given in Table \ref{['tab:params']}). The points corresponding to the exact parameters of scenarios (I) and (II) from Fig. \ref{['fig:max power']} are indicated by a purple star. The solid white lines always indicate isolines of $\mathcal{P}_\text{cool}$.
• Figure 4: $Q_\text{TUR}$, $Q_\text{KUR}$ and $Q_\text{KUR}^\text{loc}$ as functions of $\epsilon_\text{W}$ and $\delta T = T_\mathrm{L} - T_\mathrm{R}$. The points corresponding to the exact parameters of scenarios (I) and (II), see Table \ref{['tab:params']}, are indicated by a purple star. The solid white lines indicate isolines of $\mathcal{P}_\text{cool}$ in all the plots, see Fig. \ref{['fig:Pcool and Scool']}\ref{['fig:Pcool and Scool']}.
• Figure 5: Lasso plots obtained by varying $\epsilon_\text{C}$ (as indicated by the colormap), maximizing $\mathcal{P}_\text{cool}$ over $\epsilon_\text{W}$ with $\epsilon_\text{H}$ chosen such that $J^Q_\text{in}=0$. Furthermore, $U_\text{H}$ is taken as in scenarios (I) and (II) respectively, and the other parameters are the same as in Fig. \ref{['fig:max power']}. The points corresponding to the exact parameters of scenarios (I) and (II) are indicated by a purple star. The blue crosses indicate the points at which $\epsilon_\text{C} = -U_\text{C}/2$.