Non-Markovianity through entropy-based quantum thermodynamics

We introduce a generalized approach to characterize the non-Markovianity of quantum dynamical maps via breakdown of monotonicity of thermodynamic functions. By adopting an entropy-based formulation of quantum thermodynamics, we use the relationship between heat and entropy to propose a measure of non-Markovianity based on the heat flow for single-qubit quantum evolutions. This measure can be applied for unital dynamical maps that do not invert the sign of the internal energy. Under certain conditions, it can also be extended for other thermodynamic functions, such as internal energy and work flows. In this context, a natural connection between heat and quantum coherence can be identified for dynamical maps that are both unital and incoherent. As applications, we explore dissipative and nondissipative quantum dynamical processes, illustrating the compatibility between our thermodynamic quantifiers and the well-establish measure defined via quantum coherence.

Figure 1

Heat (black dotted line) and quantum coherence (red solid line) flows as a function of time for ${\vec{r}}_0=[1/2,0,1/2]$, in units such that $\gamma =0.1$ and ${\omega }_0=1$. The inset shows $\dot{Q}$ as a function of $t$.

Figure 2

Plot of $\mathbb{Q}$ as a function of ${\omega }_{c}t$ for $s=1.5$ (black dotted line) and $s=3.5$ (red solid line), with ${\omega }_0=1, r_0=1$, and $z_0=0.05$.

Figure 3

Plot of $N_{\mathbb{Q}}$ (black dotted line) and $N_C$ (red solid line) as functions of $s$ for ${\omega }_0=1$ and ${\omega }_c=1$. The inset shows $z_{\max }$ as a function of $s$.