In Szilard's engine, measurement and feedback allows to extract work from an equilibrium environment, a process otherwise forbidden by the laws of thermodynamics. Recent theoretical developments have established fluctuation theorems and thermodynamic uncertainty relations that constrain the fluctuations in Szilard's engine. These relations rely on auxiliary experimental protocols known as backward experiments. Here, we experimentally investigate the thermodynamics of Szilard's engine by implementing two distinct types of backward experiments. We verify and compare the corresponding fluctuation theorems and thermodynamic uncertainty relations associated with each protocol. Our results reveal that the entropy production inferable from measurement may serve as a more relevant quantifier of information than the widely used mutual information.
In Szilard's engine, measurement and feedback allows to extract work from an equilibrium environment, a process otherwise forbidden by the laws of thermodynamics. Recent theoretical developments have established fluctuation theorems and thermodynamic uncertainty relations that constrain the fluctuations in Szilard's engine. These relations rely on auxiliary experimental protocols known as backward experiments. Here, we experimentally investigate the thermodynamics of Szilard's engine by implementing two distinct types of backward experiments. We verify and compare the corresponding fluctuation theorems and thermodynamic uncertainty relations associated with each protocol. Our results reveal that the entropy production inferable from measurement may serve as a more relevant quantifier of information than the widely used mutual information.
Abstract In this work, we experimentally investigate the lower bound of the thermodynamic uncertainty relation (TUR) using a quantum Maxwell’s demon, specifically modeled as a Szilard engine. A quantum circuit representing the Szilard engine was designed and implemented on an IBM quantum computer that showcases the integration of quantum information processing. The circuit was executed multiple times to extract currents associated with various thermodynamic quantities, allowing for an estimation of the thermodynamic uncertainty product. TUR establishes a universal trade-off between the precision of thermodynamic currents (such as heat, work, or entropy) and entropy production rate in non-equilibrium systems, placing a universal bound on their fluctuations. Our findings indicate that the TUR’s lower bound is upheld in the quantum regime, with the uncertainty product consistently exceeding the theoretical limit of two. This result reaffirms the robustness of the thermodynamic uncertainty relation in quantum thermodynamic systems.
We propose a setup based on two coupled quantum dots where thermodynamics of a measurement can be quantitatively characterized. The information obtained in the measurement can be utilized by performing feedback in a manner apparently breaking the second law of thermodynamics. In this way the setup can be operated as a Maxwell's demon, where both the measurement and feedback are performed separately by controlling an external parameter. This is analogous to the case of the original Szilard engine. Since the setup contains both the microscopic demon and the engine itself, the operation of the whole measurement-feedback cycle can be explained in detail at the level of single realizations. In addition, we derive integral fluctuation relations for both the bare and coarse-grained entropy productions in the setup.
The laws of thermodynamics are a cornerstone for describing nanoscale and open quantum systems. However, formulating these laws for systems under continuous feedback control and under experimentally relevant conditions is challenging. In this work, we lay out a formalism for the laws of thermodynamics in an open quantum system under continuous measurement and feedback described by a Quantum Fokker Planck Master Equation. We derive expressions for work, heat, and measurement-induced energy changes, and we investigate entropy production and fluctuation theorems. We illustrate our results with a continuous version of a measurement-driven Szilard engine, as well as a work extraction scheme in a two-level system under bang-bang control. Our results provide insights into the energetics as well as the irreversibility of classical and quantum systems under continuous feedback control.
Fluctuation theorems and the second law of thermodynamics are powerful relations constraining the behavior of out-of-equilibrium systems. While there exist generalizations of these relations to feedback controlled quantum systems, their applicability is limited, in particular when considering strong and continuous measurements. In this Letter, we overcome this shortcoming by deriving a novel fluctuation theorem, and the associated second law of information thermodynamics, which remain applicable in arbitrary feedback control scenarios. In our second law, the entropy production is bounded by the coarse-grained entropy production that is inferrable from the measurement outcomes, an experimentally accessible quantity that does not diverge even under strong continuous measurements. We illustrate our results by a qubit undergoing discrete and continuous measurement, where our approach provides a useful bound on the entropy production for all measurement strengths.
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.
Recent developments of the analysis of the second law of thermodynamics by using the information theoretic quantities has led to the discovery of the so-called nonequilibrium free energy and has allowed us to formulate thermodynamic relations for arbitrary nonequilibrium initial and final states.By using the nonequilibrium free energies, we can quantify thermodynamic costs of information encoding and erasure processes as well as to quantify the extractable work from information heat engines in a unified way.In those general situations, reducing dissipation allows us to increase the extractable work from the system (or to reduce the work cost), and reducing work fluctuation allows us to narrow the work probability distribution and to extract a fluctuation-free work from the system.Suppressing both work fluctuation and dissipation as much as possible is vital to control mesoscopic and nano systems that work at the level of thermal fluctuations.Previous studies have searched for a vanishing work fluctuation protocol by using techniques of quantum information theory, known as the single-shot statistical mechanics (and sometimes called the deterministic work extraction protocol) and the vanishing dissipation protocol, known as the thermodynamically reversible protocol by using the second law of thermodynamics.In this thesis, we address issues concerning a method to control nonequilibrium systems by using fluctuation theorems and trade-off relation between work fluctuation and fluctuation in dissipation.We derive quantum fluctuation theorems under measurement and feedback control, which allow us to study how to suppress dissipation during a general quantum measurement and a feedback control.We then consider a method to suppress work fluctuation and fluctuation in dissipation simultaneously as much as possible by showing the trade-off relation between work and dissipation in terms of their standard deviations and derive an explicit protocol that achieves the lower bound of the trade-off relation.We show that the explicit protocol reproduces the deterministic work extraction protocol in the limit of vanishing work fluctuation and the thermodynamically reversible protocol in the limit of vanishing fluctuation in dissipation.