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Philipp Strasberg

Published Jan 28, 2022• 0 citations
Publisher

Abstract

Abstract The final chapter concludes the book by briefly discussing various topics we haven’t touched upon (e.g. simulating non-Markovian open quantum systems, quantum advantages in thermodynamics, resource theories) and lists some prospects for exciting future research avenues (e.g. practical applications in thermoelectrics and beyond, finding accurate reduced system descriptions, finite-bath effects).

DOI
10.1093/oso/9780192895585.003.0006

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Abstract Processes at the nanoscale happen far away from the thermodynamic limit, far from equilibrium and are dominated by fluctuations and, perhaps, even quantum effects. This book establishes a consistent thermodynamic framework for such processes by combining tools from non-equilibrium statistical mechanics and the theory of open quantum systems. The book is accessible for graduate students and of interest to all researchers striving for a deeper understanding of the laws of thermodynamics beyond their traditional realm of applicability. It puts most emphasis on the microscopic derivation and understanding of key principles and concepts as well as their interrelation. The topics covered in this book include (quantum) stochastic processes, (quantum) master equations, local detailed balance, classical stochastic thermodynamics, (quantum) fluctuation theorems, strong coupling and non non-Markovian effects, thermodynamic uncertainty relations, operational approaches, Maxwell's demon and time-reversal symmetry, among other topics. Furthermore, the book treats a few applications in detail to illustrate the general theory and its potential for practical applications. These are single-molecule pulling experiments, quantum transport and thermoelectric effects in quantum dots, the micromaser and related set-ups in quantum optics.
Quantum liquids are everywhere. This is a basic message we have tried to deliver throughout this book. But realizing the existence of quantum liquids is by no means the end of the story. An even more important issue is the fact that the various systems we have discussed in this book share common properties, precisely linked to their liquid nature. And realizing the existence of such generic trends in such different systems is a key issue by itself, as it provides a synthetic overview of whole fields of physics. In this concluding chapter, we would like to recall a few basic aspects somewhat scattered all over this book and put them again in perspective, taking for illustration a few key examples.
This chapter presents some concluding thoughts from the authors. It evokes future prospects and mentions the challenges ahead. It addresses questions such as: How far will the industry of thought experiments be carried and the quantum classical boundary pushed back? What are the odds to beat decoherence and make quantum information practical? What are the best systems to achieve these goals? Should they be reached from bottom-up, as in atomic physics, or from top-down, as in condensed matter physics?
Abstract We derive the basic laws of phenomenological non-equilibrium thermodynamics for small open systems, whose quantum nature can no longer be neglected. Emphasis is put from the beginning on deriving them from an underlying microscopic system on deriving them from an underlying microscopic system–bath picture. Commonly considered approximation schemes (wea k coupling master equations) are reviewed and their thermodynamics is studied. The zeroth law is discussed for small systems and exact identities for the entropy production, valid at strong coupling and in the non non-Markovian regime, are introduced. We discu ss the effect of finite baths even out of equilibrium and use the framework of repeated interactions to study microscopic non-equilibrium resources. The chapter concludes with the study of particle transport and thermoelectric devices, which were realized in experiments. This chapter focuses entirely on the dynamics of a system coupled to a bath without any external interventions.
Research in open quantum system dynamics has received growing interest in recent years, and its ongoing investigation has uncovered many intriguing physics departing from closed systems. A particularly useful application of the open quantum system theory is to simulate quantum dynamical processes in condensed phase materials. As the quantum degree of freedom is constantly under the influence of its thermal environment, the accurate description of the dynamics often requires non-Markovian time evolution at finite temperature. Such calculation is usually quite challenging on classical computers as extensive memory storage is required. In this work, we focus on a quantum system linearly coupled to its harmonic bath and present a path integral based quantum algorithm that time-evolves the reduced density matrix under finite temperature non-Markovian dynamics. To treat the nonunitary time evolution, the Sz.-Nagy dilation scheme is used for the conversion to unitary dynamics that can be implementable on gate-based quantum computers. The modified Hadamard test is then used to retrieve all the information of the reduced density matrix. Complexity analysis shows that the memory requirement has exponential reduction on the quantum machine whereas the runtime complexity stays roughly the same as for the classical computer. It points to the possibility of using this algorithm to simulate multilevel and multisite non-Markovian quantum dynamics that are beyond the reach of classical computers. The algorithm makes no ad hoc assumptions and extends naturally beyond Markovian and weak coupling regimes. We validated the algorithm on the quantum simulator with the spin-boson model and demonstrated its excellent agreement with the classical computer benchmark. Published by the American Physical Society 2024