Bounds on entropy production and its noise in bosonic systems

Abstract

When describing the thermodynamics of a device we are often interested in quantifying its performance, e.g. by its efficiency in converting a resource into useful output. In a general setting this is characterized by the entropy production in a resource and entropy reduction in the working substance [26]. The efficiency is often a good measure of performance when working with macroscopic machines, but when we are interested in describing nanoscale devices other aspects of performance are important aswell. This is due to phenomena such as nonthermal resources being more common due to the typical thermalization scales [26], and quantum phenomena in the transport of particles such as coherence, interference and superposition [6]. A key difference is the presence of fluctuations, which can often be of the same magnitude as average quantities in nanoscale devices. Fluctuations or noise can limit the achievable precision in the thermodynamic performance of a device, and by extension its useful applications. To understand precision in nanoscale devices is thus of crucial importance when characterising performance. In this thesis we consider multitermal nanoscale devices that can be described by scattering theory and the role fluctuations plays in their performance. The devices are modelled as reservoirs of particles connected to one dimensional leads where particles propagate coherently as waves. The leads are strongly coupled to each other in a scattering region [6]. Recently so called trade-off relations have been derived for such systems where the particles are fermions [2, 8], constraining precision. Fermions are a type of fundamental particle, obeying the Pauli exclusion principle, which states that two fermions can never occupy the same state at once. Examples of fermions are electrons and protons. In this thesis we are mainly concerned with another type of fundamental particle, namely bosons. In contrast to fermions, there is no limit to the number of bosons that can occupy the same state. This difference has multiple implications for quantum statistical mechanics and transport of the two particle types. One such difference is that bosons display bunching, they tend to “stick” together during transport which increases fluctuations, while fermions display anti-bunching, they stay apart which decreases fluctuations. In this thesis we extend the trade-off relations of Ref. [2, 8] to bosonic systems. Furthermore we make improvements to the relations of Ref. [2] which applies to both bosonic and fermionic systems. We are also able to include more quantum effects in the trade-off relations which can naturally be interpreted as bunching in the bosonic case and anti-bunching in the fermionic case. By doing this we see in which way bunching decreases precision in bosonic systems, while increasing it in fermionic systems. Finally we combine the two different types of relations to find an upper and lower bound on the total entropy production in a multiterminal device with thermal reservoirs described by scattering theory.