Bounds on entropy production and its noise in bosonic systems

Sammanfattning

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 thisis 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 macroscopicmachines, but when we are interested in describing nanoscale devices other aspects of performance areimportant aswell. This is due to phenomena such as nonthermal resources being more common due tothe typical thermalization scales [26], and quantum phenomena in the transport of particles such ascoherence, interference and superposition [6]. A key difference is the presence of fluctuations, whichcan often be of the same magnitude as average quantities in nanoscale devices. Fluctuations or noisecan limit the achievable precision in the thermodynamic performance of a device, and by extension itsuseful applications. To understand precision in nanoscale devices is thus of crucial importance whencharacterising 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 ofparticles connected to one dimensional leads where particles propagate coherently as waves. Theleads 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 thattwo 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. Incontrast to fermions, there is no limit to the number of bosons that can occupy the same state. Thisdifference 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 duringtransport which increases fluctuations, while fermions display anti-bunching, they stay apart whichdecreases 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 andfermionic systems. We are also able to include more quantum effects in the trade-off relations whichcan 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 increasingit in fermionic systems. Finally we combine the two different types of relations to find an upperand lower bound on the total entropy production in a multiterminal device with thermal reservoirsdescribed by scattering theory.