Hierarchy of entropy production and thermodynamic trade-off relations in non-Markovian systems

TL;DR

This paper explores how non-Markovian memory effects influence entropy production and thermodynamic limits, providing a hierarchy of entropy bounds and new relations for efficiency and fluctuations.

Contribution

It introduces a hierarchy of entropy production for non-Markovian systems via Markovian embedding and derives extended thermodynamic relations exploiting bath memory effects.

Findings

Entropy production in the original system bounds that of the embedded system.

Structured baths enable finite heat currents at very low entropy production.

Memory effects can reduce fluctuations and improve the precision-to-dissipation ratio.

Abstract

Non-Markovian dynamics arise when a system is coupled to a bath with finite correlation time, giving rise to memory effects that allow the bath to temporarily store and return excitations. However, how memory modifies irreversibility and whether it can be exploited to improve thermodynamic performance is not well established. We address this question by employing a Markovian embedding of generalized Langevin dynamics, in which bath memory is encoded in auxiliary modes and irreversible dissipation in a residual Markovian bath. Here we show that the entropy production defined for the original non-Markovian system upper bounds that of the embedded system, thereby establishing a hierarchy of entropy production under Markovian embedding. Leveraging this hierarchy, we derive non-Markovian extensions of the thermodynamic uncertainty relation, speed limit, and power-efficiency trade-off. For underdamed generalized Langevin systems, sufficiently structured baths allow finite heat currents at vanishingly small entropy production, whereas Carnot efficiency at finite power remains unattainable for ordinary spectral densities. In the overdamped regime, memory effects can simultaneously reduce entropy production and current fluctuations, thereby enhancing the precision-to-dissipation ratio. We further discuss the extension of the hierarchy to generic bath models and the quantum regime. These results provide a quantitative framework for exploiting memory as a thermodynamic resource and for designing energy-efficient protocols in structured environments.