A violation of the uncertainty principle implies a violation of the second law of thermodynamics

TL;DR

This paper argues that violating quantum uncertainty relations would lead to a violation of the second law of thermodynamics, thus providing a fundamental justification for the form of these relations.

Contribution

It establishes a link between quantum uncertainty relations and thermodynamic laws, showing that their violation would enable perpetual work cycles.

Findings

Violating uncertainty relations allows for thermodynamic cycles with net positive work.

Such violations would imply a breach of the second law of thermodynamics.

The results justify the form of uncertainty relations based on thermodynamic consistency.

Abstract

Uncertainty relations state that there exist certain incompatible measurements, to which the outcomes cannot be simultaneously predicted. While the exact incompatibility of quantum measurements dictated by such uncertainty relations can be inferred from the mathematical formalism of quantum theory, the question remains whether there is any more fundamental reason for the uncertainty relations to have this exact form. What, if any, would be the operational consequences if we were able to go beyond any of these uncertainty relations? We give a strong argument that justifies uncertainty relations in quantum theory by showing that violating them implies that it is also possible to violate the second law of thermodynamics. More precisely, we show that violating the uncertainty relations in quantum mechanics leads to a thermodynamic cycle with positive net work gain, which is very unlikely to exist in nature.