TY - JOUR

T1 - Continuous thermomajorization and a complete set of laws for Markovian thermal processes

AU - Lostaglio, Matteo

AU - Korzekwa, Kamil

PY - 2022

Y1 - 2022

N2 - The standard dynamical approach to quantum thermodynamics is based on Markovian master equations describing the thermalization of a system weakly coupled to a large environment, and on tools such as entropy production relations. Here we develop a framework overcoming the limitations that the current dynamical and information theory approaches encounter when applied to this setting. More precisely, we introduce the notion of continuous thermomajorization and employ it to obtain necessary and sufficient conditions for the existence of a Markovian thermal process transforming between given initial and final energy distributions of the system. These lead to a complete set of generalized entropy production inequalities including the standard one as a special case. Importantly, these conditions can be reduced to a finitely verifiable set of constraints governing nonequilibrium transformations under master equations. What is more, the framework is also constructive, i.e., it returns explicit protocols realizing any allowed transformation. These protocols use as building blocks elementary thermalizations, which we prove to be universal controls. Finally, we also present an algorithm constructing the full set of energy distributions achievable from a given initial state via Markovian thermal processes and provide a Mathematica implementation solving d=6 on a laptop computer in minutes.

AB - The standard dynamical approach to quantum thermodynamics is based on Markovian master equations describing the thermalization of a system weakly coupled to a large environment, and on tools such as entropy production relations. Here we develop a framework overcoming the limitations that the current dynamical and information theory approaches encounter when applied to this setting. More precisely, we introduce the notion of continuous thermomajorization and employ it to obtain necessary and sufficient conditions for the existence of a Markovian thermal process transforming between given initial and final energy distributions of the system. These lead to a complete set of generalized entropy production inequalities including the standard one as a special case. Importantly, these conditions can be reduced to a finitely verifiable set of constraints governing nonequilibrium transformations under master equations. What is more, the framework is also constructive, i.e., it returns explicit protocols realizing any allowed transformation. These protocols use as building blocks elementary thermalizations, which we prove to be universal controls. Finally, we also present an algorithm constructing the full set of energy distributions achievable from a given initial state via Markovian thermal processes and provide a Mathematica implementation solving d=6 on a laptop computer in minutes.

UR - http://www.scopus.com/inward/record.url?scp=85135563897&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.106.012426

DO - 10.1103/PhysRevA.106.012426

M3 - Article

AN - SCOPUS:85135563897

VL - 106

JO - Physical Review A: covering atomic, molecular, and optical physics and quantum information

JF - Physical Review A: covering atomic, molecular, and optical physics and quantum information

SN - 2469-9926

IS - 1

M1 - 012426

ER -