Quantum mean-square predictors and thermodynamics

Thermodynamic quantities, such as heat and work, are not functions of state, but rather of the process undergone by a physical system. Assessing them can therefore be difficult, since it requires probing the system at least twice. This is even more so when these quantities are to be assessed at the stochastic level. In this paper we show how to obtain optimal estimates of thermodynamic quantities solely from indirect measurement unravelings of an auxiliary system. The method always yields the true average, and the mean-squared error of the prediction is directly proportional to how well the method estimates the variance. As an application, we study energy fluctuations in a driven system, and in an avoided crossing work protocol

The Wave-Particle Duality in a Quantum Heat Engine

According to the wave-particle duality (WPD), quantum systems show both particle- and wave-like behavior, and cannot be described using only one of these classical concepts. Identifying quantum features that cannot be reproduced by any classical means is key for quantum technology. This task is often pursued by comparing the quantum system of interest to a suitable classical counterpart. However, the WPD implies that a comparison to a single classical model is generally insufficient; at least one wave and one particle model should be considered. Here we exploit this insight and contrast a bosonic quantum heat engine with two classical counterparts, one based on waves and one based on particles. While both classical models reproduce the average output power of the quantum engine, neither reproduces its fluctuations. The wave model fails to capture the vacuum fluctuations while the particle model cannot reproduce bunching to its full extent. We find regimes where wave and particle descriptions agree with the quantum one, as well as a regime where neither classical model is adequate, revealing the role of the WPD in non-equilibrium bosonic transport

Statistics of heat and work in collisional models

Na escala quântica, calor e trabalho não podem ser compreendidos somente por seus valores médios; flutuações são significantes e portanto cruciais em Termodinâmica Quântica. Para descrever correntes de energia que flutuam em sistemas quânticos, é preciso abarcar os graus de liberdade do ambiente, usualmente descartados no tratamento usual de sistemas quânticos abertos. Em tempo, modelos colisionais permitem restaurar tais graus de liberdade de maneira simples. Nesta dissertação, estendo a estatística de calor e de trabalho para o formalismo de modelos colisionais. Em particular, aplico esse formalismo a máquinas térmicas autônomas, que operam em estados estacionários fora do equilíbrio (NESS). Usando conceitos de teoria de recursos de coerência, caracterizo a dinâmica do sistem aberto de acordo com seu processamento de coerência, com particular interesse na máquina térmica de Scovil e Schulz-DuBois. Contudo, estados coerentes impõe limitações aos modelos de distribuições de trabalho, uma vez que medições comumente destroem coerência. Combinando redes Bayesianas quânticas e técnicas de estatística, desenvolvo um preditor para as flutuações do trabalho, mantendo a coerência do sistema intacta.At the quantum scale, heat and work cannot be understood solely through their average values; fluctuations are prominent and are thus crucial in Quantum Thermodynamics. To fully comprehend fluctuating energy currents in quantum systems, one has to account for environmental degrees of freedom, yet, these are commonly discarded in usual treatments of open quantum systems. Timely, collisional models permit restoring control over environments in a simple manner. In this dissertation I extend statistics of heat and work to collisional models. In particular, I apply the formalism to autonomous heat engines, which operate in non-equilibrium steady-states (NESS). Using concepts from resource theory of coherence, I characterize open-system dynamics according to its coherence processing, with particular interest in the three-level engine of Scovil and Schulz-DuBois. Yet, coherent states pose limitations in determining work distributions, since measurements often erase such property. Combining quantum Bayesian networks and insights from statistics, I develop a technique to predict work fluctuations while maintaining the system\'s coherence untouched