We combine the formalisms of diagonal entropy and Jarzynski Equality to study the thermodynamic properties of closed quantum systems. Applying this approach to a quantum harmonic oscillator, the diagonal entropy offers a notion of temperature for closed systems away from equilibrium, and allows computing free-energy profiles. We also apply this approach to a hard-core boson lattice model, and discuss measures how to estimate temperature, entropy and measure work distribution functions. This technique offers a path to investigate the non-equilibrium quantum dynamics by means of performing work in a series of quenches.
We combine the formalisms of diagonal entropy and Jarzynski Equality to study the thermodynamic properties of closed quantum systems. Applying this approach to a quantum harmonic oscillator, the diagonal entropy offers a notion of temperature for closed systems away from equilibrium, and allows computing free-energy profiles. We also apply this approach to a hard-core boson lattice model, and discuss measures how to estimate temperature, entropy and measure work distribution functions. This technique offers a path to investigate the non-equilibrium quantum dynamics by means of performing work in a series of quenches.
We propose a combination between the theory of diagonal entropy representing far-from-equilibrium ensembles and Jarzynski Equality to explore thermalization effects on thermodynamic quantities such as temperature, entropy, mechanical work and free-energy changes. Applying the theory to a quantum harmonic oscillator, we find that diagonal entropy offers a definition of temperature for closed systems far from equilibrium, and a better sampling of reaction pathways than the conventional von Neumann entropy. We also apply the theory to a many-body system of hard-core boson lattice, and discuss the ideas of how to estimate temperature, entropy and measure work distribution functions. The theory suggests a powerful technique to study non-equilibrium dynamics in quantum systems by means of performing work in a series of quenches.
In this work we present a formalism to describe non equilibrium conditions in systems with a discretized energy spectrum, such as quantum systems. We develop a formalism based on a combination of Gibbs-Shannon entropy and information thermodynamics that arrives to a generalization of the De-Brujin identity applicable to discrete and non-symmetric distributions. This allows to define the concept of a thermodynamic temperature with a different, albeit complementary meaning to the equilibrium kinetic temperature of a system. The theory is applied to Bosonic and Fermionic cases represented by an harmonic oscillator and a single energy state, respectively. We show that the formalism correctly recovers known results at equilibrium, then we demonstrate an application to a genuine non equilibrium state: a coherent quantum oscillator.
A diagonal entropy, which depends only on the diagonal elements of the system's density matrix in the energy representation, has been recently introduced as the proper definition of thermodynamic entropy in out-of-equilibrium quantum systems. We study this quantity after an interaction quench in lattice hard-core bosons and spinless fermions, and after a local chemical potential quench in a system of hard-core bosons in a superlattice potential. The former systems have a chaotic regime, where the diagonal entropy becomes equivalent to the equilibrium microcanonical entropy, coinciding with the onset of thermalization. The latter system is integrable. We show that its diagonal entropy is additive and different from the entropy of a generalized Gibbs ensemble, which has been introduced to account for the effects of conserved quantities at integrability.
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.
A central open question in quantum thermodynamics is the identification of thermodynamic entropy away from equilibrium. Although thermodynamic entropy coincides with the von Neumann entropy for a Gibbs state at equilibrium, the thermodynamic role of quantum coherence generated during nonequilibrium evolution remains unclear. Here, we show that von Neumann entropy does not, in general, represent the thermodynamic entropy governing heat exchange in coherent nonequilibrium quantum systems. By integrating the resource theory of quantum coherence with thermodynamic principles, we develop a general framework for nonequilibrium quantum thermodynamics. We identify thermodynamic entropy with the energy entropy derived from energy-measurement statistics and introduce a dynamical temperature extending the equilibrium concept to nonequilibrium states. Consequently, we obtain an exact entropy-balance relation separating the entropy flux associated with heat exchange from the coherence-loss contribution to entropy production, establishing an operational connection between quantum coherence, heat flow, and total entropy change. Unlike approaches relying on equilibrium reference states or stationary Gibbs ensembles, our framework uses instantaneous dynamical quantities and remains valid throughout transient nonequilibrium evolution. It provides consistent dynamical definitions of temperature, work, heat, and free energy. Applying the formalism to an exactly solvable open quantum system, we show that the first and second laws hold throughout transient evolution and that equilibrium thermodynamics emerges dynamically in the weak-coupling long-time limit. Our results establish a unified framework for coherent nonequilibrium quantum thermodynamics and suggest opportunities for controlling heat dissipation through coherence engineering in quantum thermal technologies.
Fluctuation relations allow for the computation of equilibrium properties, like free energy, from an ensemble of non-equilibrium dynamics simulations. Computing them for quantum systems, however, can be difficult, as performing dynamic simulations of such systems is exponentially hard on classical computers. Quantum computers can alleviate this hurdle, as they can efficiently simulate quantum systems. Here, we present an algorithm utilizing a fluctuation relation known as the Jarzynski equality to approximate free energy differences of quantum systems on a quantum computer. We discuss under which conditions our approximation becomes exact, and under which conditions it serves as a strict upper bound. Furthermore, we successfully demonstrate a proof-of-concept of our algorithm using the transverse field Ising model on a real quantum processor. The free energy is a central thermodynamic property that allows one to compute virtually any equilibrium property of a physical system. Thus, as quantum hardware continues to improve, our algorithm may serve as a valuable tool in a wide range of applications including the construction of phase diagrams, prediction of transport properties and reaction constants, and computer-aided drug design in the future.