Non-Markovianity and negative entropy production rates

Area of Science:

• * Theoretical physics
• * Non-equilibrium thermodynamics
• * Quantum mechanics

Background:

• * Entropy production quantifies irreversibility in open systems, typically positive.
• * Negative entropy production rates are sometimes observed and linked to non-Markovianity.
• * A precise understanding of this link and its conditions is lacking.

Purpose of the Study:

• * To precisely establish the conditions under which a negative entropy production rate implies non-Markovianity.
• * To develop a unified theoretical framework for finite-time thermodynamics of diverse dynamics.
• * To investigate the role of the instantaneous fixed point in non-Markovian dynamics.

Main Methods:

• * Analysis of system dynamics coupled to a single heat bath.
• * Unified treatment of coarse-grained Markovian master equations and classical Hamiltonian dynamics.
• * Investigation of the quantum analogue of classical Hamiltonian dynamics.

Main Results:

• * Negative entropy production implies non-Markovianity under specific, defined conditions.
• * A unified framework is presented for analyzing Markovian and classical Hamiltonian dynamics.
• * The quantum version of the classical Hamiltonian dynamics result does not hold, despite formal equivalence.

Conclusions:

• * A consistent theoretical framework is provided for studying finite-time thermodynamics.
• * The study clarifies the precise link between negative entropy production and non-Markovianity.
• * The findings are crucial for understanding irreversibility in complex quantum and classical systems.