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

Understand

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 new 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.