The theory of thermodynamics describes the ways in which energy can be traded between macroscopic objects. It is one of the most successful scientific theories, with many useful applications to chemistry, physics and engineering. For instance, the celebrated second law places restrictions on the efficiency of machines and heat engines.
Advances in technology allow us to imagine a future in which we design devices that employ quantum effects such as coherence or entanglement. While such quantum devices can be studied by solving their equation of motion, it is also of interest to develop a thermodynamic description of their operation. For such microscopic setups, some of the assumption used in classical thermodynamics break down, due to effects such as coherence or strong coupling between a system and its environment.
In a recent paper, Raam Uzdin and Saar Rahav from the Schulich faculty of chemistry developed an approach that allows the derivation of thermodynamic-like inequalities for such quantum processes. When the setup is composed of initially uncoupled and thermal subsystems, the approach leads to the Clausius’ formulation of the second law. Crucially, the approach allows one to derive additional inequalities and is valid under much more general conditions.
As examples for the application of the approach, the authors derive both lower and upper bounds for correlations generated between a system and its environment. It is also shown that violation of the inequalities can be used to detect heat leaks in quantum operations, or alternatively external tampering in the dynamics. This theoretical approach will be a valuable tool for the analysis of thermodynamic-like processes in small quantum systems, a rapidly developing experimental field.
This study was published in Physical Review X. For more information, see https://journals.aps.org/prx/abstract/10.1103/PhysRevX.8.021064
Figure 1: Detection of a heat leak in a device performing quantum CNOT operation. Some of the inequalities derived for the system detect the heat leak much sooner than it would be detected based on violation of the second law.