This article traces the development of fluctuation theory and its deep connection to irreversibility, from equilibrium to near-equilibrium, and finally to far-from-equilibrium systems. Classical fluctuation theorems, which capture the statistical behaviour of thermodynamic systems far from equilibrium, are now well established. Their quantum counterparts, however, remain an active area of research. In this review, we highlight recent advances by linking quantum fluctuation theorems with linear response theory, offering new insights into the nature of quantum fluctuations and irreversibility in the near-equilibrium regime. Particular emphasis is placed on dissipated work in quantum systems as a pathway to observing non-classical effects in quantum thermodynamics. Understanding quantum fluctuations is not only essential for clarifying the foundations of irreversibility but also crucial for the development of novel quantum technologies, including quantum computers, sensors, and metrological devices.
This article traces the development of fluctuation theory and its deep connection to irreversibility, from equilibrium to near-equilibrium, and finally to far-from-equilibrium systems. Classical fluctuation theorems, which capture the statistical behaviour of thermodynamic systems far from equilibrium, are now well established. Their quantum counterparts, however, remain an active area of research. In this review, we highlight recent advances by linking quantum fluctuation theorems with linear response theory, offering new insights into the nature of quantum fluctuations and irreversibility in the near-equilibrium regime. Particular emphasis is placed on dissipated work in quantum systems as a pathway to observing non-classical effects in quantum thermodynamics. Understanding quantum fluctuations is not only essential for clarifying the foundations of irreversibility but also crucial for the development of novel quantum technologies, including quantum computers, sensors, and metrological devices.
Abstract We have previously developed this framework in the context of static response, here we will generalize this perspective to dynamic response, and the evolution between distinct thermal equilibrium states. Of particular importance will be the derivation of the fluctuation-dissipation theorem, which relates the response of a system to its time dependent fluctuations, clarifying an equivalence between how a system responds to a small perturbation and how it regresses back to equilibrium in the absence of a perturbation. With this framework we can develop linear models of relaxation, classically and quantum mechanically, and derive equa- tions of motion suitable for describing the dynamics of thermal ensembles held at fixed temperature rather than fixed energy. These models are Gaussian, and approximate the dynamical correlations of interacting systems. These effective equations of motion are rendered stochastic due to the incomplete description of the microscopic degrees of freedom that evolve the system.
The purpose of this work is to discuss recent progress in deriving the fundamental laws of thermodynamics (0th, 1st and 2nd-law) from nonequilibrium quantum statistical mechanics. Basic thermodynamic notions are clarified and different reversible and irreversible thermodynamic processes are studied from the point of view of quantum statistical mechanics. Special emphasis is put on new adiabatic theorems for steady states close to and far from equilibrium, and on investigating cyclic thermodynamic processes using an extension of Floquet theory.
The thermodynamics of quantum systems driven out of equilibrium has attracted increasing attention in the last decade, in connection with quantum information and statistical physics, and with a focus on non-classical signatures. While a first approach can deal with average thermodynamics quantities over ensembles, in order to establish the impact of quantum and environmental fluctuations during the evolution, a continuous quantum measurement of the open system is required. Here, we provide an introduction to the general theoretical framework to establish and interpret the thermodynamics for quantum systems whose nonequilibrium evolution is continuously monitored. We review the formalism of quantum trajectories and its consistent application to the thermodynamic scenario, where primary quantities such as work, heat, and entropy production can be defined at the stochastic level. The connection to irreversibility and fluctuation theorems is also discussed together with some recent developments, and we provide some simple examples to illustrate the general theoretical framework.
Thermodynamics is a phenomenological theory describing the energy conversion of work and heat. At its origins thermodynamics was developed in order to understand and improve heat engines. In conventional thermodynamics, however, only such processes are completely describable which are slow enough to keep the system of interest in an equilibrium state with its thermal environment at all times. On the contrary, all real physical processes are accompanied by non-equilibrium phenomena. These are mathematically described with the help of the irreversible entropy production, i.e. the dissipated work divided by the temperature of the bath. The second law of thermodynamics merely states that the irreversible entropy production is on average always positive. The modern trend of miniaturization, however, leads to smaller and smaller devices. On short length scales thermal noise as well as quantum fluctuations become important. Thus, usual thermodynamic quantities as work and heat acquire stochastic nature. Moreover, in the quantum regime a completely new theory had to be invented, since classical notions of work and heat are no longer valid. The present dissertation contributes to this prevailing field by the derivation of analytical expressions for the entropy production in open and closed quantum system far from thermal equilibrium. The theoretical treatment is motivated by an experimental point of view. The obtained results were derived from the reduced dynamics of the quantum mechanical system, which may be coupled to a thermal bath. To this end, it was dealt with methods and approaches of statistical physics, conventional thermodynamics, quantum information theory and the theory of open quantum systems. In this dissertation the most important physical systems are treated. First, an isolated system is considered before later on a heat bath is included. The limit of weak as well as of strong coupling are analyzed in detail. For isolated systems it turns out that a geometric approach is able to capture the thermodynamic properties, completely. To this end, the irreversible entropy production is sharply estimated from below by the angle between the real non-equilibrium state and the corresponding equilibrium one. Further, it is shown that the Heisenberg uncertainty relation for energy and time can be formulated more precisely in terms of that angle. As experimental system cold ion traps are introduced, in which the theoretical predictions can be verified. For weakly coupled systems, then, the irreversible entropy production is identified and a fluctuation theorem is derived by merely thermodynamic arguments. As experimental system we, again, propose the cold ion traps, where the heat bath can be simulated with the help of LASER light. In the limit of strong coupling a semiclassical description of the reduced quantum system is discussed. Again, an analytically exact expression for the entropy production and the corresponding fluctuation theorem is derived. A physical system, in which strong coupling to the environment can be analyzed, is given by Josephson junctions. This dissertation discusses the entropy production for isolated, weakly coupled, and overdamped quantum systems. For these physical regimes analytical relation are derived and experimental systems proposed, with which the predictions can be verified.
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.
This thesis is a study of non-equilibrium phenomena in quantum systems. Emphasis is given to the recently derived non-equilibrium fluctuation theorems, which relate the non-equilibrium response of a system to its equilibrium thermodynamic properties. We investigate the validity and importance of these theorems, from both a theoretical and experimental perspective, in systems ranging from a single atom to an ensemble of interacting particles. We also investigate the potential role of quantum dynamics in biological processes.