Universal Scaling Bounds on a Quantum Heat Current

TL;DR

This paper establishes fundamental bounds on how the heat current in a quantum system scales with system size, providing insights into the limits of quantum thermodynamic device performance.

Contribution

It derives new scaling bounds on quantum heat currents, including a universal $ heta(L^3)$ bound and a more feasible $ heta(L^2)$ bound under certain conditions, with implications for quantum thermodynamics.

Findings

Heat current scales at most as $ heta(L^3)$ for extensive Hamiltonians.

A $ heta(L^2)$ bound is derived for systems with limited energy difference noise.

Superradiance can saturate the $ heta(L^2)$ bound.

Abstract

We derive new bounds on a heat current flowing into a quantum $L$-particle system coupled with a Markovian environment. By assuming that a system Hamiltonian and a system-environment interaction Hamiltonian are extensive in $L$, we show that the absolute value of the heat current scales at most as $\Theta (L^3)$ in a limit of large $L$. Also, we present an example that saturates this bound in terms of scaling: non-interacting particles globally coupled with a thermal bath. However, the construction of such system requires many-body interactions induced by the environment, which may be difficult to realize with the current technology. To consider more feasible cases, we focus on a class of system where any non-diagonal elements of the noise operator (derived from the system-environment interaction Hamiltonian) become zero in the system energy basis, if the energy difference is beyond a certain value $\Delta E$. Then, for $\Delta E = \Theta (L^0)$, we derive another scaling bound $\Theta (L^2)$ on the absolute value of the heat current, and the so-called superradiance belongs to a class to saturate this bound. Our results are useful to evaluate the best achievable performance of quantum-enhanced thermodynamic devices, which contain far-reaching applications for such as quantum heat engines, quantum refrigerators and quantum batteries.