New exact results about the nonequilibrium thermodynamics of open quantum systems at arbitrary timescales are obtained by considering all possible variations of initial conditions of a system, its environment, and correlations between them. First we obtain a new quantum-information theoretic equality for entropy production, valid for an arbitrary initial joint state of system and environment. For any finite-time process with a fixed initial environment, we then show that the contraction of the system's distinction -- relative to the minimally dissipative state -- exactly quantifies its thermodynamic dissipation. The quantum component of this dissipation is the change in coherence relative to the minimally dissipative state. Implications for quantum state preparation and local control are explored. For nonunitary processes -- like the preparation of any particular quantum state -- we find that mismatched expectations lead to divergent dissipation as the actual initial state becomes orthogonal to the anticipated one.
We derive general relations between maximum power, maximum efficiency, and minimum dissipation regimes from linear irreversible thermodynamics. The relations simplify further in the presence of a particular symmetry of the Onsager matrix, which can be derived from detailed balance. The results are illustrated on a periodically driven system and a three terminal device subject to an external magnetic field.
A dynamical theory for the organization and dissipation of a current in a non-equilibrium fluid near equilibrium is presented. This is based on the Lyapunov exponents of the phase space of the system.
We investigate the open dynamics of a chain of interacting spins using the quantized version of the GENERIC equation from classical out-of-equilibrium thermodynamics. We focus on both equilibrium and nonequilibrium scenarios for chains of different sizes. While in the equilibrium case we demonstrate thermal equilibration to the correct many-body Gibbs density matrix, in the nonequilibrium dynamics we show a ballistic-to-diffusive transition in the steady-state energy current and a scaling that is consistent with Fourier's law of heat transfer.
The fluctuation-dissipation theorem is a fundamental result in statistical physics that establishes a connection between the response of a system subject to a perturbation and the fluctuations associated with observables in equilibrium. Here we derive its version within a resource-theoretic framework, where one investigates optimal quantum state transitions under thermodynamic constraints. More precisely, we first characterise optimal thermodynamic distillation processes, and then prove a relation between the amount of free energy dissipated in such processes and the free energy fluctuations o…
We analyze the stochastic evolution and dephasing of a qubit within the quantum jump (QJ) approach. It allows one to treat individual realizations of inelastic processes, and in this way it provides solutions, for instance, to problems in quantum thermodynamics and distributions in statistical mechanics. As a solvable example, we study a qubit in the weak dissipation limit, and demonstrate that dephasing and relaxation render the Jarzynski and Crooks fluctuation relations (FRs) of non-equilibrium thermodynamics intact. On the contrary, the standard two-measurement protocol, taking into account…
In this work we explore the use of thermodynamic length to improve the performance of experimental protocols. In particular, we implement Landauer erasure on a driven electron level in a semiconductor quantum dot, and compare the standard protocol in which the energy is increased linearly in time with the one coming from geometric optimisation. The latter is obtained by choosing a suitable metric structure, whose geodesics correspond to optimal finite-time thermodynamic protocols in the slow driving regime. We show experimentally that geodesic drivings minimise dissipation for slow protocols, …
Reformulating constitutive relation in terms of gradient dynamics (being derivative of a dissipation potential) brings additional information on stability, metastability and instability of the dynamics with respect to perturbations of the constitutive relation, called CR-stability. CR-instability is connected to the loss of convexity of the dissipation potential, which makes the Legendre-conjugate dissipation potential multivalued and causes dissipative phase transitions, that are not induced by non-convexity of free energy, but by non-convexity of the dissipation potential. CR-stability of th…
In this work, we expose the role of environment, confinement and external magnetic field ($B$) in determining the low temperature thermodynamic behaviour in the context of cyclotron motion of a charged oscillator with anomalous dissipative coupling involving the momentum instead of the much studied coordinate coupling. Explicit expressions for different quantum thermodynamic functions (QTF) are obtained at low temperatures for different quantum heat bath characterized by spectral density function, $μ(ω)$. The power law fall of different QTF are in conformity with third law of thermodynamics. B…
A free particle coupled to a heat bath can exhibit a number of thermodynamic anomalies like a negative specific heat or reentrant classicality. These low-temperature phenomena are expected to be modified at very low temperatures where finite-size effects associated with the discreteness of the energy spectrum become relevant. In this paper, we explore in which form the thermodynamic anomalies of the free damped particle appear for a damped harmonic oscillator. Since the discreteness of the oscillator's energy spectrum is fully accounted for, the results are valid for arbitrary temperatures. As…
How much free energy is irreversibly lost during a thermodynamic process? For deterministic protocols, lower bounds on energy dissipation arise from the thermodynamic friction associated with pushing a system out of equilibrium in finite time. Recent work has also bounded the cost of precisely moving a single degree of freedom. Using stochastic thermodynamics, we compute the total energy cost of an autonomously controlled system by considering both thermodynamic friction and the entropic cost of precisely directing a single control parameter. Our result suggests a challenge to the usual unders…
The direction of the steady-state heat currents across a generic quantum system connected to multiple baths may be engineered so as to realize virtually any thermodynamic cycle. In spite of their versatility such continuous energy-conversion systems are generally unable to operate at maximum efficiency due to non-negligible sources of irreversible entropy production. In this paper we introduce a minimal model of irreversible absorption chiller. We identify and characterize the different mechanisms responsible for its irreversibility, namely heat leaks and internal dissipation, and gauge their …
Thermodynamics serves as a universal means for studying physical systems from an energy perspective. In recent years, with the establishment of the field of stochastic and quantum thermodynamics, the ideas of thermodynamics have been generalized to small fluctuating systems. Independently developed in mathematics and statistics, the optimal transport theory concerns the means by which one can optimally transport a source distribution to a target distribution, deriving a useful metric between probability distributions, called the Wasserstein distance. Despite their seemingly unrelated nature, a…
We revisit here the effect of quantum dissipation on the much - studied problem of Landau diamagnetism, and analyze the results in the light of the third law of thermodynamics. The case of an additional parabolic potential is separately assessed. We find that dissipation arising from strong coupling of the system to its environment qualitatively alters the low-temperature thermodynamic attributes such as the entropy and the specific heat.
We explore the thermodynamic geometry of a simple system that models the bistable dynamics of nucleic acid hairpins in single molecule force-extension experiments. Near equilibrium, optimal (minimum-dissipation) driving protocols are governed by a generalized linear response friction coefficient. Our analysis and simulations demonstrate that the friction coefficient of the driving protocols is sharply peaked at the interface between metastable regions, which leads to minimum-dissipation protocols that drive rapidly within a metastable basin, but then linger longest at the interface, giving the…
The thermodynamic uncertainty relations provide a universal trade-offs between entropy dissipation rate and fluctuations in transport current. This relation has been mostly used to estimate a minimum entropy dissipation rate by experimentally measuring current fluctuations. Here we consider joint currents and show that such uncertainty relations cannot be simultaneously achievable for any two currents, which leads to a potential underestimation of the minimum entropy dissipation rate.
We establish a stochastic thermodynamics for a Fermionic level driven by a time-dependent force and interacting with initially thermalized levels playing the role of a reservoir. The driving induces consecutive avoided crossings between system and reservoir levels described within Landau-Zener theory. We derive the resulting system dynamics and thermodynamics and identify energy, work, heat, entropy and dissipation. Our theory perfectly reproduces the numerically exact quantum work statistics obtained using a two point measurements approach of the total energy and provides an explicit expressi…
Biological and engineered systems operate by coupling function to the transfer of heat and/or particles down a thermal or chemical gradient. In idealized \textit{deterministically} driven systems, thermodynamic control can be exerted reversibly, with no entropy production, as long as the rate of the protocol is made slow compared to the equilibration time of the system. Here we consider \textit{fully realizable, entropically driven} systems where the control parameters themselves obey rules that are reversible and that acquire directionality in time solely through dissipation. We show that whe…
The Minimum Rate of Dissipation Principle (MRDP) affirms that, for time-independent boundary conditions, a thermodynamic system evolves towards a steady-state with the least possible dissipation. In this note, examples of diffusion processes of two solutes in an isothermal system are analyzed in detail. In particular, we consider the relaxation of the system when the metric tensor (i.e. the Onsager matrix) is constant and when the Onsager coefficients weakly depend on the spatial derivatives of the concentrations. We show that, to leading order, during the relaxation towards a steady-state, th…
Stochastic thermodynamics provides a useful set of tools to analyze and constrain the behavior of far from equilibrium systems. In this paper, we report an application of ideas from stochastic thermodynamics to the problem of membrane growth. Non-equilibrium forcing of the membrane can cause it to buckle and undergo a morphological transformation. We show how ideas from stochastic thermodynamics, in particular the recently derived thermodynamic uncertainty relations, can be used to phenomenologically describe and constrain the parameters required to excite morphological changes during a non-eq…
We derive a relation between the dissipation in a stochastic dynamics and the Wasserstein distance. We show that the minimal amount of dissipation required to transform an initial state to a final state during a diffusion process is given by the Wasserstein distance between the two states, divided by the total time of the process. This relation implies a lower bound on the dissipation for any diffusion process in terms of its initial and final state. Using a lower bound on the Wasserstein distance, we further show that we can give a lower bound on the dissipation in terms of only the mean and …
Fluctuations of thermodynamic quantities become non-negligible and play an important role when the system size is small. We develop finite-time thermodynamics of fluctuations in microscopic heat engines whose environmental temperature and mechanical parameter are driven periodically in time. Within the slow-driving regime, this formalism universally holds in a coarse-grained time scale whose resolution is much longer than the correlation time of the fluctuations, and is shown to be consistent with the relation analogous to the fluctuation-dissipation relation. Employing a geometric argument, a…
A Unified Nonequilibrium Framework: Thermodynamic Distance, Dissipation, and Stationary Laws via Effective State Count, Variational Stationarity, and Thermodynamic Bounds
We characterize finite-time thermodynamic processes of multidimensional quadratic overdamped systems. Analytic expressions are provided for heat, work, and dissipation for any evolution of the system covariance matrix. The Bures-Wasserstein metric between covariance matrices naturally emerges as the local quantifier of dissipation. General principles of how to apply these geometric tools to identify optimal protocols are discussed. Focusing on the relevant slow-driving limit, we show how these results can be used to analyze cases in which the experimental control over the system is partial.
We propose a conservation-dissipation formalism (CDF) for coarse-grained descriptions of irreversible processes. This formalism is based on a stability criterion for non-equilibrium thermodynamics. The criterion ensures that non-equilibrium states tend to equilibrium in long time. As a systematic methodology, CDF provides a feasible procedure in choosing non-equilibrium state variables and determining their evolution equations. The equations derived in CDF have a unified elegant form. They are globally hyperbolic, allow a convenient definition of weak solutions, and are amenable to existing nu…
The effects of dissipation on the thermodynamic properties of nonlinear quantum systems are approached by the path-integral method in order to construct approximate classical-like formulas for evaluating thermal averages of thermodynamic quantities. Explicit calculations are presented for one-particle and many-body systems. The effects of the dissipation mechanism on the phase diagram of two-dimensional Josephson arrays is discussed.
The high accuracy exhibited by biological information transcription processes is due to kinetic proofreading, i.e., by a mechanism which reduces the error rate of the information-handling process by driving it out of equilibrium. We provide a consistent thermodynamic description of enzyme-assisted assembly processes involving competing substrates, in a Master Equation framework. We introduce and evaluate a measure of the efficiency based on rigorous non-equilibrium inequalities. The performance of several proofreading models are thus analyzed and the related time, dissipation and efficiency vs…
Thermodynamic uncertainty relations (TURs) represent one of the few broad-based and fundamental relations in our toolbox for tackling the thermodynamics of nonequilibrium systems. One form of TUR quantifies the minimal energetic cost of achieving a certain precision in determining a nonequilibrium current. In this initial stage of our research program, our goal is to provide the quantum theoretical basis of TURs using microphysics models of linear open quantum systems where it is possible to obtain exact solutions. In paper [Dong \textit{et al.}, Entropy {\bf 24}, 870 (2022)], we show how TURs…
The fluctuation-dissipation-theorem connects equilibrium to mildly (linearly) perturbed situations in a thermodynamic manner: It involves the observable of interest and the entropy production caused by the perturbation. We derive a relation which connects responses of arbitrary order in perturbation strength to correlations of entropy production of lower order, thereby extending the fluctuation-dissipation-theorem to cases far from equilibrium in a thermodynamic way. The relation is validated and studied for a 4-state-model.
The D-wave processor is a partially controllable open quantum system which exchanges energy with its surrounding environment (in the form of heat) and with the external time dependent control fields (in the form of work). Despite being rarely thought as such, it is a thermodynamic machine. Here we investigate the properties of the D-Wave quantum annealers from a thermodynamical perspective. We performed a number of reverse-annealing experiments on the D-Wave 2000Q via the open access cloud server Leap, with the aim of understanding what type of thermal operation the machine performs, and quant…
Thermodynamic uncertainty relations (TURs) set fundamental bounds on the fluctuation and dissipation of stochastic systems. Here, we examine these bounds, in experiment and theory, by exploring the entire phase space of a cyclic information engine operating in a non-equilibrium steady state. Close to its maximal efficiency, we find that the engine violates the original TUR. This first experimental demonstration of TUR violation agrees with recently proposed softer bounds: The engine satisfies two generalized TUR bounds derived from the detailed fluctuation theorem with feedback control and ano…
Producing a large current typically requires large dissipation, as is the case in electric conduction, where Joule heating is proportional to the square of the current. Stochastic thermodynamics offers a framework to study nonequilibrium thermodynamics of small fluctuating systems, and quite recently, microscopic derivations and universal understanding of the trade-off relation between the current and dissipation have been put forward. Here we establish a universal framework clarifying how quantum coherence affects the trade-off between the current and dissipation: a proper use of coherence en…
We consider quantum nonlinear many-body systems with dissipation described within the Caldeira-Leggett model, i.e., by a nonlocal action in the path integral for the density matrix. Approximate classical-like formulas for thermodynamic quantities are derived for the case of many degrees of freedom, with general kinetic and dissipative quadratic forms. The underlying scheme is the pure-quantum self-consistent harmonic approximation (PQSCHA), equivalent to the variational approach by the Feynman-Jensen inequality with a suitable quadratic nonlocal trial action. A low-coupling approximation permi…
Thermodynamics of nanoscale devices is an active area of research. Despite their noisy surrounding they often produce mechanical work (e.g. micro-heat engines), display rectified Brownian motion (e.g. molecular motors). This invokes research in terms of experimentally quantifiable thermodynamic efficiencies. Here, a Brownian particle is driven by a harmonic confinement with time-periodic contraction and expansion. The system produces work by being alternately (time-periodically) connected to baths with different dissipations. We analyze the system theoretically using stochastic thermodynamics.…
Thermodynamics with thermodynamic variable first-passage time. II. Dynamics of explosive boiling of superheated liquid, critical indices, fractional calculus
Institute for Nuclear Research, pr. Nauki, 47 Kiev, Ukraine（乌克兰国家核科学研究所）
The driving force of the dynamical system can be decomposed into the gradient of a potential landscape and curl flux (current). The fluctuation-dissipation theorem (FDT) is often applied to near equilibrium systems with detailed balance. The response due to a small perturbation can be expressed by a spontaneous fluctuation. For non-equilibrium systems, we derived a generalized FDT that the response function is composed of two parts: (1) a spontaneous correlation representing the relaxation which is present in the near equilibrium systems with detailed balance; (2) a correlation related to the …
A fundamental problem in modern thermodynamics is how a molecular-scale machine performs useful work, while operating away from thermal equilibrium without excessive dissipation. To this end, we derive a friction tensor that induces a Riemannian manifold on the space of thermodynamic states. Within the linear-response regime, this metric structure controls the dissipation of finite-time transformations, and bestows optimal protocols with many useful properties. We discuss the connection to the existing thermodynamic length formalism, and demonstrate the utility of this metric by solving for op…
The standard {\em system-plus-reservoir} approach used in the study of dissipative systems can be meaningfully generalized to a dissipative coupling involving the momentum, instead of the coordinate: the corresponding equation of motion differs from the Langevin equation, so this is called {\em anomalous} dissipation. It occurs for systems where such coupling can indeed be derived from the physical analysis of the degrees of freedom which can be treated as a dissipation bath. Starting from the influence functional corresponding to anomalous dissipation, it is shown how to derive the effective …
In classical Markov jump processes, current fluctuations can only be reduced at the cost of increased dissipation. To explore how quantum effects influence this trade-off, we analyze the uncertainty of steady-state currents in Markovian open quantum systems. We first consider three instructive examples and then systematically minimize the product of uncertainty and entropy production for small open quantum systems. As our main result, we find that the thermodynamic cost of reducing fluctuations can be lowered below the classical bound by coherence. We conjecture that this cost can be made arbi…
Nonequilibrium information thermodynamics determines the minimum energy dissipation to reliably erase memory under time-symmetric control protocols. We demonstrate that its bounds are tight and so show that the costs overwhelm those implied by Landauer's energy bound on information erasure. Moreover, in the limit of perfect computation, the costs diverge. The conclusion is that time-asymmetric protocols should be developed for efficient, accurate thermodynamic computing. And, that Landauer's Stack -- the full suite of theoretically-predicted thermodynamic costs -- is ready for experimental tes…
