ABSTRACT: Starting in undergraduate statistical physics, we study small systems that thermalize by exchanging quantities with large environments. The exchanged quantities—heat, particles, electric charge, etc.—are conserved globally, and the thermalization helps define time’s arrow. If quantum, the quantities are represented by Hermitian operators. We often assume implicitly that the operators commute with each other—for instance, in derivations of the thermal state’s form. Yet operators’ ability to not commute underlies quantum phenomena such as uncertainty principles and measurement disturbance. What happens if thermodynamic conserved quantities fail to commute with each other? This question, mostly overlooked for decades, came to light recently at the intersection of quantum information theory and thermodynamics. Noncommutation of conserved thermodynamic quantities has been found to enhance average entanglement, decrease entropy-production rates, alter basic assumptions behind thermalization, and more. This growing subfield illustrates how 21st-century quantum information science is extending 19th-century thermodynamics.

Majidy, Braasch, Lasek, Upadhyaya, Kalev, and NYH, Nat. Rev. Phys. 5, 689-698 (2023). https://www.nature.com/articles/s42254-023-00641-9