Reversing Heat Flow by Coherence in a Multipartite Quantum System

Abstract

The second law of thermodynamics dictates that heat flows spontaneously from a high-temperature entity to a lower-temperature one. Yet, recent advances have demonstrated that quantum correlations between a system and its thermal environment can induce a reversal of heat flow, challenging classical thermodynamic expectations. Here, we experimentally demonstrate that internal quantum coherence in a multipartite spin system can also reverse heat flow, without relying on initial correlations with the environment. Under the collision model with cascade interaction, we verify that both the strength and the phase of the coherence term determine the direction and magnitude of energy transfer. These results enable precise control of heat flow using only local quantum properties.

Figures (13)

• Figure 1: Collision model with cascade interaction. The system and the bath are uncorrelated. The system consists of multiple subsystems and is assumed to be in a thermal state at a higher temperature, while the thermal bath comprises an infinite number of identical particles at a lower temperature. For a single collision, each subsystem sequentially interacts with a bath particle in a fixed order, such as $S_1$–$S_2$–$S_3\cdots$. In this scenario, heat flows from the higher-temperature subsystems to the lower-temperature bath. However, injecting coherence into the system can modify this behavior and even reverse the direction of heat flow.
• Figure 2: (a) Molecular structure of crotonic acid used as the four-qubit NMR system. The nuclear spins of C$_1$, C$_2$, C$_3$, and C$_4$ are designated as subsystems S$_1$, S$_2$, S$_3$, and bath particle R, respectively. (b) Quantum circuit implementing the collision model with cascade interaction. It consists of three segments corresponding to the stages outlined in the main text. The first two operations initialize the bath particle. The system state with controlled coherence is prepared using temporal averaging, which involves applying different operations at distinct times. The thermal contact stage includes $n$ partial SWAP operations, with $n=3$ in our experiment.
• Figure 3: (a) Overview of energy transfer dynamics in the thermal contact. (b)-(d) Time evolution of the energy of each subsystem for different initial coherence values. The energy change in $S_3$ is consistently larger than that in $S_2$, while $S_1$ follows the behavior of standard thermal contact. (e)-(g) Heat transfer and free energy changes in the system. Heat flowing from system to bath is defined as positive, with the system prepared at higher local temperature. With coherence $c = 0.5e^{i\pi}$, heat tends to flow from the bath to the system; in contrast, for the same coherence amplitude but with phase $\alpha = 0$, heat flows from the system to the bath. (h)-(j) ATs of $S_1$, $S_2$, and $S_3$ as functions of interaction time, corresponding to the experimental settings in (b)-(d). The $x$-axis is expressed in units of a single subsystem–bath interaction, and the maximum time shown corresponds to 100 full collision sequences. The dashed line indicates the temperature of the bath, which is equal to its AT. Symbols denote experimental data; lines represent numerical simulations.
• Figure 4: (a) Heat flow behavior in $S_2$ and $S_3$ under equal initial temperatures. The coherence terms are set as $c_{12} = 0.3$, $c_{23} = c_{13} = -0.5$, leading to opposite heat flow directions in the two subsystems. (b) Reversed heat flow under a temperature gradient. The subsystem temperatures are $T_2 = \delta/k_{\mathrm{B}}$, $T_R= 0.9\delta/k_{\mathrm{B}}$ and $T_3 = 0.8\delta/k_{\mathrm{B}}$, with coherence set as $c_{12}=-0.5$ and $c_{23} = c_{13} = 0.5$. Despite the gradient, the hotter $S_2$ absorbs heat while the colder $S_3$ releases it. (c) Energy dynamics under different interaction sequences. The coherence is fixed at $c_{12} = -0.5$, $c_{13} = -0.1$, and $c_{23} = 0.5$. Changing the order of interaction among subsystems reverses the direction of heat flow in key ordinal positions, such as the second ($S_2$ for both sequence) and the final ($S_3$ for forward sequence and $S_1$ for reverse sequence) interacting spin. The other parameters are the same as in Fig. \ref{['Fig3']}.
• Figure 5: Structure and parameter.