Established heat engines in quantum regime can be modeled with various quantum systems as working substances. For example, in the non-relativistic case, we can model the heat engine using infinite potential well as a working substance to evaluate the efficiency and work done of the engine. Here, we propose quantum heat engine with a relativistic particle confined in the one-dimensional potential well as working substance. The cycle comprises of two isothermal processes and two potential well processes of equal width, which forms the quantum counterpart of the known isochoric process in classical nature. For a concrete interpretation about the relation between the quantum observables with the physically measurable parameters (like the efficiency and work done), we develop a link between the thermodynamic variables and the uncertainty relation. We have used this model to explore the work extraction and the efficiency of the heat engine for a relativistic case from the standpoint of uncertainty relation, where the incompatible observables are the position and the momentum operators. We are able to determine the bounds (the upper and the lower bounds) of the efficiency of the heat engine through the thermal uncertainty relation.

According to the Landauer principle, any logically irreversible process accompanies entropy production, which results in heat dissipation in the environment. Erasing of information, one of the primary logically irreversible processes, has a lower bound on heat dissipated into the environment, called the Landauer bound (LB). However, the practical erasure processes dissipate much more heat than the LB. Recently, there have been a few experimental investigations to reach this bound both in the classical and quantum domains. There has also been a spate of activities to enquire about this LB in finite time, with finite-size heat baths, non-Markovian and nonequilibrium environments in the quantum regime where the effects of fluctuations and correlation of the systems with the bath can no longer be ignored. This article provides a comprehensive review of the recent progress on the LB, which serves as a fundamental principle in the thermodynamics of computation. We also provide a perspective for future endeavors in these directions. Furthermore, we review the recent explorations toward establishing energetic bounds of a computational process. We also discuss the thermodynamic aspects of error correction, which is an indispensable part of information processing and computations. In doing so, we briefly discuss the basics of these fields to provide a complete picture.

Quantum cycles in established heat engines can be modeled with various quantum systems as working substances. For example, a heat engine can be modeled with an infinite potential well as the working substance to determine the efficiency and work done. However, in this method, the relationship between the quantum observables and the physically measurable parameters—i.e., the efficiency and work done—is not well understood from the quantum mechanics approach. A detailed analysis is needed to link the thermodynamic variables (on which the efficiency and work done depends) with the uncertainty principle for better understanding. Here, we present the connection of the sum uncertainty relation of position and momentum operators with thermodynamic variables in the quantum heat engine model. We are able to determine the upper and lower bounds on the efficiency of the heat engine through the uncertainty relation.