Abstract
As previously demonstrated, the entropy production—a key quantity characterizing the irreversibility of thermodynamic processes—is related to generation of correlations between degrees of freedom of the system and its thermal environment. This raises the question of whether such correlations are of a classical or quantum nature, namely, whether they are accessible through local measurements on the correlated degrees of freedom. We address this problem by considering fermionic and bosonic Gaussian systems. We show that, for fermions, the entropy production is mostly quantum due to the parity superselection rule that restricts the set of physically allowed measurements to projections on the Fock states, thus significantly limiting the amount of classically accessible correlations. In contrast, in bosonic systems a much larger amount of correlations can be accessed through Gaussian measurements. Specifically, while the quantum contribution may be important at low temperatures, in the high-temperature limit the entropy production corresponds to purely classical position-momentum correlations. Our results demonstrate an important difference between fermionic and bosonic systems regarding the existence of a quantum-to-classical transition in the microscopic formulation of the entropy production. They also show that entropy production can be mainly caused by quantum correlations even in the weak coupling limit, which admits a description in terms of classical rate equations for state populations, as well as in the low particle density limit, where the transport properties of both bosons and fermions converge to those of classical particles.
- Received 24 March 2023
- Accepted 2 June 2023
DOI:https://doi.org/10.1103/PRXQuantum.4.020353
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Physical processes in the observed world often have a preferred direction heat flows from the hot to the cold body and not vice versa. This phenomenon is referred to as thermodynamic irreversibility and is described by the second law of thermodynamics. It is however not fully explained how irreversibility emerges from the laws of quantum mechanics, which are reversible, that is, have no preferred direction.
In previous works the origins of irreversibility have been related to the generation of correlations (mutual interdependence) between the thermodynamic system and microscopic degrees of freedom in its environment. Here we study whether such correlations can be described within the framework of classical mechanics or are intrinsically quantum. We show that the answer is different for two classes of particles: fermions (for example, electrons) and bosons (for example, phonons, describing vibrations of atomic lattices). For fermionic systems, the microscopic origin of irreversibility is mostly quantum. Interestingly, this is true even when their dynamics can be effectively described using classical methods. In contrast, for bosons, it becomes mostly classical for high temperatures; such a phenomenon is referred to as the quantum-to-classical transition.
Our work demonstrates that the microscopic origin of thermodynamic irreversibility may depend on the nature of the physical system considered. It also shows that certain thermodynamic processes can have a fundamentally quantum origin even when their outward manifestations can be described in a purely classical way. This sheds new light on the role of quantum mechanics in observed physical phenomena.
