Exchange fluctuation theorem for correlated quantum systems

We extend the exchange fluctuation theorem for energy exchange between thermal quantum systems beyond the assumption of molecular chaos, and describe the nonequilibrium exchange dynamics of correlated quantum states. The relation quantifies how the tendency for systems to equilibrate is modified in high-correlation environments. In addition, a more abstract approach leads us to a “correlation fluctuation theorem”. Our results elucidate the role of measurement disturbance for such scenarios. We show a simple application by finding a semiclassical maximum work theorem in the presence of correlations. We also present a toy example of qubit-qudit heat exchange, and find that non-classical behaviour such as deterministic energy transfer and anomalous heat flow are reflected in our exchange fluctuation theorem.

Figure 1

Why correlations matter: two systems $A$ and $B$ are at temperatures $T_A$ and $T_B$ initially. The generalized XFT, Eq. (18), is plotted as a function $f\left(x\right)$ of a correlation parameter $x$ and the mutual information $I\left(x\right)$ (light gray curve) is also included. As $I\left(x\right)$ increases, the XFT deviates from its value in the “molecular chaos” assumption where $x=0$ (dashed line). The likelihood of heat flow direction is indicated by the gray arrows for different $x$. A circle round the arrows indicates the uncorrelated regime $x=0$. For some $x$, backward heat flow can be completely suppressed. Top figure: a two-qubit system where $B$ is hotter than $A$; $f\left(x\right)$ is a single black curve. Bottom figure: a qubit-qutrit system at equal temperature. Unlike two qubits, the XFT is only defined by a range (light gray region) and we see, even though $T_A=T_B$, correlations can induce heat flow on average, thereby violating the principle of detailed balance.