Thermodynamic bound on current fluctuations in coherent conductors

TL;DR

This paper establishes a universal thermodynamic bound on current fluctuations in coherent conductors, linking fluctuations to entropy production and dissipation, applicable to multi-terminal quantum transport systems.

Contribution

It introduces a general bound on large-deviation functions of particle currents in quantum conductors based solely on mean current and entropy production, extending thermodynamic uncertainty relations.

Findings

The bound applies to multi-terminal setups with symmetric transmission.

For typical fluctuations, it recovers known thermodynamic uncertainty relations.

A quantum dot chain model demonstrates the bound can be saturated.

Abstract

We derive a universal bound on the large-deviation functions of particle currents in coherent conductors. This bound depends only on the mean value of the relevant current and the total rate of entropy production required to maintain a non-equilibrium steady state, thus showing that both typical and rare current fluctuations are ultimately constrained by dissipation. Our analysis relies on the scattering approach to quantum transport and applies to any multi-terminal setup with arbitrary chemical potential and temperature gradients, provided the transmission coefficients between reservoirs are symmetric. This condition is satisfied for any two-terminal system and, more generally, when the dynamics of particles within the conductor are symmetric under time-reversal. For typical current fluctuations, we recover a recently derived thermodynamic uncertainty relation for coherent transport. To illustrate our theory, we analyze a specific model comprising two reservoirs connected by a chain of quantum dots, which shows that our bound can be saturated asymptotically.