The nonequilibrium thermodynamics of interacting quantum many-body systems is investigated within the framework of thermal time-dependent density functional theory using a generalized linear-response formulation for the full quantum work statistics. A first-principles route is established to reconstruct the relaxation function that underlies linear-response theory, thereby moving beyond phenomenological descriptions and enabling a consistent evaluation of all moments of the dissipated-work distribution in interacting systems. The predictive power of the approach is demonstrated for the Hubbard model subject to a staggered external potential, where the evolution of the relaxation dynamics across the Mott-to-band-insulator crossover reveals how distinct many-body phases shape the out-of-equilibrium thermodynamic response. These results provide a microscopic and transferable framework for quantum thermodynamics in correlated systems, bridging thermal density functional theory and nonequilibrium work statistics.
The nonequilibrium thermodynamics of interacting quantum many-body systems is investigated within the framework of thermal time-dependent density functional theory using a generalized linear-response formulation for the full quantum work statistics. A first-principles route is established to reconstruct the relaxation function that underlies linear-response theory, thereby moving beyond phenomenological descriptions and enabling a consistent evaluation of all moments of the dissipated-work distribution in interacting systems. The predictive power of the approach is demonstrated for the Hubbard model subject to a staggered external potential, where the evolution of the relaxation dynamics across the Mott-to-band-insulator crossover reveals how distinct many-body phases shape the out-of-equilibrium thermodynamic response. These results provide a microscopic and transferable framework for quantum thermodynamics in correlated systems, bridging thermal density functional theory and nonequilibrium work statistics.
We consider a quantum system driven out of equilibrium via a small Hamiltonian perturbation. Building on the paradigmatic framework of linear response theory (LRT), we derive an expression for the full generating function of the dissipated work. Remarkably, we find that all information about the distribution can be encoded in a single quantity, the standard relaxation function in LRT, thus opening up new ways to use phenomenological models to study nonequilibrium fluctuations in complex quantum systems. Our results establish a number of refined quantum thermodynamic constraints on the work statistics that apply to regimes of perturbative but arbitrarily fast protocols, and do not rely on assumptions such as slow driving or weak coupling. Finally, our approach uncovers a distinctly quantum signature in the work statistics that originates from underlying zero-point energy fluctuations. This causes an increased dispersion of the probability distribution at short driving times, a feature that can be probed in efforts to witness nonclassical effects in quantum thermodynamics.
Understanding the thermodynamic properties of many-body quantum systems and their emergence from microscopic laws is a topic of great significance due to its profound fundamental implications and extensive practical applications. Recent advances in experimental techniques for controlling and preparing these systems have increased interest in this area, as they have the potential to drive the development of quantum technologies. In this study, we present a density-functional-theory approach to extract detailed information about the statistics of work and the irreversible entropy associated with quantum quenches at finite temperature. Specifically, we demonstrate that these quantities can be expressed as functionals of thermal and out-of-equilibrium densities, which may serve as fundamental variables for understanding finite-temperature many-body processes. We, then, apply our method to the case of the inhomogeneous Hubbard model, showing that our density-functional-theory-based approach can be usefully employed to unveil the distinctive roles of interaction and external potential on the thermodynamic properties of such a system. Published by the American Physical Society 2024
We propose a description of nonequilibrium systems via a simple protocol that combines exchange-correlation potentials from density functional theory with self-energies of many-body perturbation theory. The approach, aimed to avoid double counting of interactions, is tested against exact results in Hubbard-type systems, with respect to interaction strength, perturbation speed and inhomogeneity, and system dimensionality and size. In many regimes, we find significant improvement over adiabatic time dependent density functional theory or second Born nonequilibrium Green's function approximations. We briefly discuss the reasons for the residual discrepancies, and directions for future work.
In this thesis, we study nonequilibrium statistical mechanics from a geometric perspective.In particular, we (i) examine the relation between quantum information geometry and linear response theory, and (ii) analyze nonequilibrium processes in thermodynamic control and derive a geometric expression for work.The first original study in this thesis is to understand quantum information geometry based on linear response theory.We show that the quantum Fisher information can be determined by measuring the linear response functions.For that purpose, we generalize the fluctuationdissipation theorem, and establish the quantitative relation between linear response functions and the generalized covariance, which contains the same amount of information on the quantum state.Based on the generalized fluctuation-dissipation theorem, we can determine the generalized covariance and the quantum Fisher information by measuring linear response functions, such as the dynamical susceptibilities and the complex admittances for all frequencies.We demonstrate that our result is applicable to experimental determination of the skew information, and a validation of skew information-based uncertainty relations.The second original study is on the analysis of work in thermodynamic control.We extend the thermodynamic metric-based expression for work into two directions.One is to obtain a systematic expansion of the average work from a phenomenological argument, and the other is to obtain an expansion of the work distribution for overdamped Langevin systems.First, we derive a systematic expansion of the work in terms of a small parameter ϵ that characterizes how slowly we control the system.The leading-order contribution is given by the thermodynamic metric expression.The next leading-order contributions to the thermodynamic metric contribution can be detected by comparing the excess work in a forward control and a backward control, and are predicted to scale as 1/T 2 as a function of the total control time T .Since the expansion is derived without assuming any specific microscopic dynamics, it is valid as long as the perturbation series expansion is valid.Finally, we examine the work distribution in overdamped Langevin systems.We derive the time evolution equation for the moment generating function of the work, and solve it from the lower-order contributions in ϵ.The O(ϵ) contribution to the generating function reproduces two known facts: the work distribution is Gaussian, and the average work is given by the thermodynamic metric.When we take up to O(ϵ 2 ) contributions into account, the work distribution exhibits nonzero skewness, which means that the fluctuation-dissipation relation is violated with scaling 1/T 2 .Furthermore, from the analytic calculation with numerical supports, we conjecture that the nth cumulant of the work scales as 1/T n-1 for n ≥ 1.
The thermodynamic behavior of out-of-equilibrium quantum systems in finite-time dynamics encompasses the description of energy fluctuations, which dictates a series of the system's physical properties. In addition, strong interactions in many-body systems strikingly affect the energy-fluctuation statistics along a nonequilibrium dynamics. By driving transient currents to oppose the precursor to the metal-Mott-insulator transition in a diversity of dynamical regimes, we show how increasing many-body interactions dramatically affect the statistics of energy fluctuations and, consequently, the extractable work distribution of finite Hubbard chains. Statistical properties of such distributions as its skewness with its impressive change across the transition can be related to irreversibility and entropy production. Even for slow driving rates, the quasi quantum phase transition hinders equilibration, increasing the process irreversibility, and inducing strong features in the work distribution. In the Mott-insulating phase, the work fluctuation-dissipation balance gets modified with the irreversible entropy production dominating over work fluctuations. Because of this, effects of an interaction-driven quantum phase transition on thermodynamic quantities and irreversibility must be considered in the design of protocols in small-scale devices for application in quantum technology. Eventually, such many-body effects can also be employed in work extraction and refrigeration protocols on a quantum scale.
We develop a nonequilibrium time-dependent functional theory of coupled interacting fields in terms of the Liouvillian quantum field dynamics. In this theory the expectation values of the appropriate field operators are treated as the functional variables. Thus, the formalism proposed here goes beyond the existing time-dependent density-functional method, in that we now have a mixed-state multivariable dynamical theory. A large class of condensed matter problems, with the given initial condition that the system be in thermodynamic equilibrium and subjected to time-dependent external forces, can now be examined. In particular, we formulate the self-consistent coupled equations for the electron, ion, and the electromagnetic fields. The above formalism provides a firm physical and mathematical basis for time-dependent dynamical simulation procedures such as those envisaged in the Car-Parrinello approach by replacing the fictitious Lagrangian by a precise action principle. The theory involves a certain functional representing the mutual interactions and correlations among these fields. In parallel with this, we also generalize the Baym \ensuremath{\Phi}-derivable method in many-body theory to investigate the class of problems mentioned above. This involves a functional of the exact one-particle Green functions. We compare the two methods and suggest the use of the latter in the former scheme as a way of going beyond the simple mean-field schemes. We illustrate the utility of the framework by citing a variety of illustrative examples.