Entropic bounds on currents in Langevin systems

TL;DR

This paper establishes entropic bounds on currents in Langevin systems, revealing fundamental tradeoffs between power and efficiency in heat engines and ratchets, applicable to both overdamped and underdamped dynamics.

Contribution

It derives a universal entropic bound on generalized currents in Langevin systems, linking entropy production to power-efficiency tradeoffs in various thermodynamic models.

Findings

Bound on currents in Langevin systems based on entropy production

Power-efficiency tradeoff relations for ratchets and heat engines

Additional constraints on Onsager matrix for weak driving

Abstract

We derive a bound on generalized currents for Langevin systems in terms of the total entropy production in the system and its environment. For overdamped dynamics, any generalized current is bounded by the total rate of entropy production. We show that this entropic bound on the magnitude of generalized currents imposes power-efficiency tradeoff relations for ratchets in contact with a heat bath: Maximum efficiency---Carnot efficiency for a Smoluchowski-Feynman ratchet and unity for a flashing or rocking ratchet---can only be reached at vanishing power output. For underdamped dynamics, while there may be reversible currents that are not bounded by the entropy production rate, we show that the output power and heat absorption rate are irreversible currents and thus obey the same bound. As a consequence, a power-efficiency tradeoff relation holds not only for underdamped ratchets but also for periodically driven heat engines. For weak driving, the bound results in additional constraints on the Onsager matrix beyond those imposed by the Second Law. Finally, we discuss the connection between heat and entropy in a non-thermal situation where the friction and noise intensity are state-dependent.