One of the most important problems in quantum thermodynamics is how to distinguish work and heat in autonomous quantum systems. In this paper, work and heat are defined through the following criterion, i.e., work is the energy that cannot change the entropy of the energy resource, and satisfies the Jarzynski equality, while heat does not. Two kinds of definitions satisfying the two corresponding requirements are proposed and demonstrated, and the consistency condition of the two kinds is given. Through the first definition, the problem of entropy production is investigated. A model study is also presented to verify the proposal.
One of the most important problems in quantum thermodynamics is how to distinguish work and heat in autonomous quantum systems. In this paper, work and heat are defined through the following criterion, i.e., work is the energy that cannot change the entropy of the energy resource, and satisfies the Jarzynski equality, while heat does not. Two kinds of definitions satisfying the two corresponding requirements are proposed and demonstrated, and the consistency condition of the two kinds is given. Through the first definition, the problem of entropy production is investigated. A model study is also presented to verify the proposal.
In this paper, unambiguous redefinitions of heat and work are presented for quantum thermodynamic systems. We will use genuine reasoning based on which Clausius originally defined work and heat in establishing thermodynamics. The change in the energy which is accompanied by a change in the entropy is identified as heat, while any change in the energy which does not lead to a change in the entropy is known as work. It will be seen that quantum coherence does not allow all the energy exchanged between two quantum systems to be only of the heat form. Several examples will also be discussed. Finally, it will be shown that these refined definitions will strongly affect the entropy production of quantum thermodynamic processes giving new insight into the irreversibility of quantum processes.
The question of with what we associate work and heat in a quantum thermodynamic process has been extensively discussed, mostly for systems with time-dependent Hamiltonians. In this paper, we aim to investigate the energy exchanged between two quantum systems through interaction where the Hamiltonian of the system is time-independent. An entropy-based re-definitions of heat and work are presented for these quantum thermodynamic systems therefore an entropy-based formalism of both the first and the second laws of thermodynamics are introduced. We will use the genuine reasoning based on which Clausius originally defined work and heat. The change in the energy which is accompanied by a change in the entropy is identified as heat, while any change in the energy which does not lead to a change in the entropy is known as work. It will be seen that quantum coherence does not allow all the energy exchanged between two quantum systems to be only of the heat form. Several examples will also be discussed. Finally, we will examine irreversibility from our entropy-based formalism of quantum thermodynamics.
In open quantum systems, a clear distinction between work and heat is often challenging, and extending the quantum Jarzynski equality to systems evolving under general quantum channels beyond unitality remains an open problem in quantum thermodynamics. In this Letter, we introduce well-defined notions of guessed quantum heat and guessed quantum work, by exploiting the one-time measurement scheme, which only requires an initial energy measurement on the system alone. We derive a modified quantum Jarzynski equality and the principle of maximum work with respect to the guessed quantum work, which requires the knowledge of the system only. We further show the significance of guessed quantum heat and work by linking them to the problem of quantum hypothesis testing.
Quantum work is usually determined from two projective measurements of the energy at the beginning and at the end of a thermodynamic process. However, this paradigm cannot be considered thermodynamically consistent as it does not account for the thermodynamic cost of these measurements. To remedy this conceptual inconsistency we introduce a paradigm that relies only on the expected change of the average energy given the initial energy eigenbasis. In particular, we completely omit quantum measurements in the definition of quantum work, and hence quantum work is identified as a thermodynamic quantity of only the system. As main results we derive a modified quantum Jarzynski equality and a sharpened maximum work theorem in terms of the information free energy. A comparison of our results with the standard approach allows one to quantify the informational cost of projective measurements.
A consistent theory of non-equilibrium thermodynamics for Markovian open quantum systems has been developed in the late seventies in analogy with Classical Irreversible Thermodynamics. The time-evolution of these open systems is usually described by means of effective master equations in Lindblad form, that turn out to be reliable when there is a separation of time-scales between system and environment, such that memory effects are negligible and the so-called Markovian approximation is justified. In this framework, the variations of energy and entropy in the system are consistently described, distinguishing between heat and work contributions and providing a statement of the second law of thermodynamics as positivity of the entropy production.\nHowever, there is empirical evidence that many physical systems like photosynthetic complexes,\nopto-mechanical resonators and superconducting qubits, just to mention a few, experience more general non-Markovian dynamics. The formulation of the laws of thermodynamics in a non-Markovian setting is matter of current research and represents the main topic of the present work. As a first step, we show that the entropy production defined as in the Markovian case can be negative for a class of non-Markovian dynamics. We argue that this outcome should not be interpreted as a violation of the second law of thermodynamics because the environment must be explicitly taken into account in the balance of entropy in the non-Markovian setting. In order to justify this claim we adopt a more general point of view, studying a closed bipartite quantum system, such that each of the two subsystems plays the role of a finite environment out of equilibrium for the other one. We concentrate on the balance of energy first and construct an effective Hamiltonian for each subsystem using physically reasonable requirements; then we define heat and work as in the standard Markovian treatment, with the effective Hamiltonian replacing the free Hamiltonian. It turns out that, in our framework, the work power is perfectly balanced between subsystems, while the correlations can store a part of energy locally inaccessible and exchange it with both subsystems in the form of heat.\nConcerning the balance of entropy, a quite general formulation of the second law of thermodynamics can be given as follows: under the assumption of a factorized initial state for the compound system, the sum of the total variations of the entropies in the two subsystems is always nonnegative. We show with an explicit example that this general formulation does not correspond to the statement presented in the framework of Markovian master equations, which should not be considered a priori the second law of thermodynamics.\nIn the last part of the thesis we concentrate of the so-called fluctuation relations, that are results extending the thermodynamic formalism beyond the behavior of average quantities. After reviewing the main theoretical outcomes, such as the Jarzynski equality and the Crooks fluctuation theorem, we describe a proposal to access experimentally the work performed on an ensemble of diatomic molecules by a time-dependent electric field coupled with their vibrational degree of freedom. This procedure could then be used to test the quantum Jarzynski equality. With respect to the results so far appeared in the literature, in which the left-hand side of the equality is inferred from an experiment and the right-hand side is computed according to a model, in our proposed setting we should be able to estimate from the experiment both the left-hand side and the right-hand side of the equality, independently.
Traditional quantum thermodynamic frameworks associate work to energy exchanges induced by unitary transformations generated by external controls, and heat to energy exchanges induced by bath interaction. Recently, a framework was introduced aiming at extending the thermodynamic formalism to genuine quantum settings, also referred to as autonomous quantum systems: free from external controls, only quantum systems interacting with each other. In this paper, we apply such a thermodynamic framework to common experimental situations of interacting quantum systems. In situations where traditional frameworks detect only heat exchanges, the recent autonomous thermodynamic framework points at work exchanges based on two mechanisms: population inversion and coherence generation / consumption. Such mechanisms are well known in the literature for being related to work expenditure and extraction, in particular in relation with ergotropy, which emphasizes the relevance of the autonomous framework and the limitations of traditional ones. Furthermore, the autonomous framework also identifies a genuine non-unitary mechanism of work exchange related to athermality. %, also pointed out as a resource for work extraction. Finally, in the semi-classical limit, the autonomous framework identifies all energy exchanges as pure work, but distinguishes between local work and interaction energy.
Our results show that the autonomous framework provides a refined analysis of work exchange mechanisms in the quantum realm and serves as a consistent approach to analyze thermodynamic processes in realistic quantum devices.