This work presents a unified dissipaton-equation-of-motion (DEOM) theory and its evaluations on the Helmholtz free energy change due to the isotherm mixing of two isolated subsystems. One is a local impurity and another is a nonlocal Gaussian bath. DEOM constitutes a fundamental theory for such open quantum mixtures. To complete the theory, we construct also the imaginary-time DEOM formalism via an analytical continuation of dissipaton algebra, which would be limited to equilibrium thermodynamics. On the other hand, the real-time DEOM deals with both equilibrium structural and nonequilibrium dynamic properties. Its combination with the thermodynamic integral formalism would be a viable and accurate means to both equilibrium and transient thermodynamics. As illustrations, we report the numerical results on a spin--boson system, with elaborations on the underlying anharmonic features, the thermodynamic entropy versus the von Neumann entropy, and an indication of "solvent-cage" formation. Beside the required asymptotic equilibrium properties, the proposed transient thermodynamics also supports the basic spontaneity criterion.
This Perspective presents a comprehensive account of the dissipaton theories developed in our group since 2014, including the physical picture of dissipatons and the phase-space dissipaton algebra. The dissipaton-equation-of-motion-space (DEOM-space) formulations cover the Schrödinger picture, the Heisenberg picture, and further the imaginary-time DEOM. Recently developed are also the dissipaton theories for studying equilibrium and nonequilibrium thermodynamic mixing processes. The Jarzynski equality and Crooks relation are accurately reproduced numerically. It is anticipated that dissipaton …
The physical origin of the backbendings in the equations of state of finite but not necessarily small systems is studied in the Ising model with fixed magnetization (IMFM) by means of the topological properties of the observable distributions and the analysis of the largest cluster with increasing lattice size. Looking at the convexity anomalies of the IMFM thermodynamic potential, it is shown that the order of the transition at the thermodynamic limit can be recognized in finite systems independently of the lattice size. General statistical mechanics arguments and analytical calculations sugg…
In a thermodynamical process, the dissipation or production of entropy can only be positive or zero according to the second law of thermodynamics. However the laws of thermodynamics are applicable to large systems in the thermodynamic limit. Recently a fluctuation theorem known as the Transient Fluctuation Theorem (TFT) which generalizes the second law of thermodynamics even for small systems has been proposed. This theorem has been tested in small systems such as a colloidal particle in an optical trap. We report for the first time an analogous experimental study of TFT in a spatially extende…
Physical systems that power motion and create structure in a fixed amount of time dissipate energy and produce entropy. Whether living or synthetic, systems performing these dynamic functions must balance dissipation and speed. Here, we show that rates of energy and entropy exchange are subject to a speed limit -- a time-information uncertainty relation -- imposed by the rates of change in the information content of the system. This uncertainty relation bounds the time that elapses before the change in a thermodynamic quantity has the same magnitude as its initial standard deviation. From this…
In this report I discuss fluctuation theorems and transient violations of the second law of thermodynamics in small systems. Special emphasis is placed on free-energy recovery methods in the framework of non-equilibrium single-molecule pulling experiments. The treatment is done from a unified theoretical-experimental perspective and emphasizes how these experiments contribute to our understanding of the thermodynamic behavior of small systems
We obtain exact results for the recently discovered finite-time thermodynamic uncertainty relation in a stochastically driven system with non-Gaussian work statistics, both in the steady state and transient regimes, by obtaining exact expressions for any moment of the dissipated work at arbitrary times. The uncertainty function (the Fano factor of the dissipated work) is bounded from below by $2k_BT$ as expected, for all times $τ$, in both steady state and transient regimes. The lower bound is reached at $τ=0$ as well as when certain system parameters vanish (corresponding to an equilibrium st…
The total entropy production of stochastic systems can be divided into three quantities. The first corresponds to the excess heat, whilst the second two comprise the house-keeping heat. We denote these two components the transient and generalised house-keeping heat and we obtain an integral fluctuation theorem for the latter, valid for all Markovian stochastic dynamics. A previously reported formalism is obtained when the stationary probability distribution is symmetric for all variables that are odd under time reversal which restricts consideration of directional variables such as velocity.
Electrical circuits with transient elements can be good examples of systems where non--steady irreversible processes occur, so in the same way as a steady state energy converter, we use the formal construction of the first order irreversible thermodynamic (FOIT) to describe the energetics of these circuits. In this case, we propose an isothermic model of two meshes with transient and passive elements, besides containing two voltage sources (which can be functions of time); this is a non--steady energy converter model. Through the Kirchhoff equations, we can write the circuit phenomenological e…
We investigate transient version of the recently discovered thermodynamic uncertainty relation (TUR) which provides a precision-cost trade-off relation for certain out-of-equilibrium thermodynamic observables in terms of net entropy production. We explore this relation in the context of energy transport in a bipartite setting for three exactly solvable toy model systems (two coupled harmonic oscillators, two coupled qubits and a hybrid coupled oscillator-qubit system) and analyze the role played by the underlying statistics of the transport carriers in TUR. Interestingly, for all these models,…
In the last ten years, a number of ``Conventional Fluctuation Theorems'' have been derived for systems with deterministic or stochastic dynamics, in a transient or in a non-equilibrium stationary state. These theorems gave explicit expressions for the ratio of the probability to find the system with a certain value of entropy (or heat) production to that of finding the opposite value. A similar theorem for the fluctuations of the work done on a system has recently been demonstrated experimentally for a simple system in a transient state, consisting of a Brownian particle in water, confined by …
The transient network model of Green-Tobolsky [1946], Yamamoto [1956] and Tanaka-Edwards [1992] is formulated within the frame of thermodynamics of irreversible processes, using as a fundamental quantity the chemical potential associated to the connection of strands to the network and treating these connections as chemical-like reactions. All thermodynamic quantities are thus naturally defined in and out of equilibrium. Constitutive equations are derived, giving the stress and the heat production as functions of the thermomechanical history. The Clausius-Duhem inequality, stating that the sour…
We study the entropy time evolution of a quantum mechanical model, which is frequently used as a prototype for Anderson's localization. Recently Latora and Baranger [V. Latora, M. Baranger, Phys. Rev.Lett. 82, 520(1999)] found that there exist three entropy regimes, a transient regime of passage from dynamics to thermodynamics, a linear in time regime of entropy increase, namely a thermodynamic regime of Kolmogorov kind, and a saturation regime. We use the non-extensive entropic indicator recently advocated by Tsallis [ C. Tsallis, J. Stat. Phys. 52, 479 (1988)] with a mobile entropic index q,…
A central result that arose in applying information theory to the stochastic thermodynamics of nonlinear dynamical systems is the Information-Processing Second Law (IPSL): the physical entropy of the universe can decrease if compensated by the Shannon-Kolmogorov-Sinai entropy change of appropriate information-carrying degrees of freedom. In particular, the asymptotic-rate IPSL precisely delineates the thermodynamic functioning of autonomous Maxwellian demons and information engines. How do these systems begin to function as engines, Landauer erasers, and error correctors? Here, we identify a m…
A general nonequilibrium thermodynamic theory is developed for time-dependent Langevin dynamics, starting from the common definition of nonequilibrium Gibbs entropy. It is shown that the notations appearing in the First and the Second Law of thermodynamics could be consistently applied to transient nonequilibrium processes. We find out a general equality representing the energy balance relation for the system, and further an explicit mathematical interpretation for the extended form of the Second Law is proposed, which only comes into existence in the time-dependent case. More applications to …
Do negative absolute temperatures matter physics and specifically Statistical Physics? We provide evidence that we can certainly answer positively to this vexata quaestio. The great majority of models investigated by statistical mechanics over almost one century and a half exhibit positive absolute temperature, because their entropy is a nondecreasing function of energy. Since more than half a century ago it has been realized that this may not be the case for some physical systems as incompressible fluids, nuclear magnetic chains, lasers, cold atoms and optical waveguides. We review these exam…
Thermodynamic uncertainty relations (TURs) bound the dissipation in non-equilibrium systems from below by fluctuations of an observed current. Contrasting the elaborate techniques employed in existing proofs, we here prove TURs directly from the Langevin equation. This establishes the TUR as an inherent property of overdamped stochastic equations of motion. In addition, we extend the transient TUR to currents and densities with explicit time-dependence. By including current-density correlations we, moreover, derive a new sharpened TUR for transient dynamics. Our arguably simplest and most dire…
There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time-reversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations between entropy production, phase-space contraction and time-reversal starting from a deterministic dynamics. Both closed and open systems, in the transient and in the steady regime, are considered. The main result identifies under general conditions the statistical mechanical entropy production as the source term of time-reversal breaking in the path space me…
This paper has been withdrawn by the author. For the reason, see the bottom paragraph of this abstract. By generalizing Tasaki's work on the second law of thermodynamics for an adiabatic process between two equilibrium states of a macroscopic quantum compound system, we obtain an extension of the second law to a transient adiabatic process that takes a macroscopic quantum compound system consisting of a system of interest and two heat reservoirs from an initial equilibrium state to a final non-equilibrium state, where the system of interest is in a steady heat conduction state. For the system …
We study subdiffusive overdamped Brownian ratchets periodically rocked by an external zero-mean force in viscoelastic media within the framework of non-Markovian Generalized Langevin equation (GLE) approach and associated multi-dimensional Markovian embedding dynamics. Viscoelastic deformations of the medium caused by the transport particle are modeled by a set of auxiliary Brownian quasi-particles elastically coupled to the transport particle and characterized by a hierarchy of relaxation times which obey a fractal scaling. The most slowly relaxing deformations which cannot immediately follow…
We analyze multiple new issues concerning activated relaxation in glassy hard sphere fluids and molecular and polymer liquids based on the Elastically Collective Nonlinear Langevin Equation (ECNLE) theory. By invoking a high temperature reference state, a near universality of the apparent dynamic localization length scale is predicted for liquids of widely varying fragility, a result that is relevant to recent simulation studies and quasi-elastic neutron scattering measurements. In contrast, in the same format strongly non-universal behavior is found for the activation barrier that controls lo…
Using the recently derived Dissipation Theorem and a corollary of the Transient Fluctuation Theorem (TFT), namely the Second Law Inequality, we derive the unique time independent, equilibrium phase space distribution function for an ergodic Hamiltonian system in contact with a remote heat bath. We prove under very general conditions that any deviation from this equilibrium distribution breaks the time independence of the distribution. Provided temporal correlations decay, and the system is ergodic, we show that any nonequilibrium distribution that is an even function of the momenta, eventually…
This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states after infinite-time evolution, irrespective of dynamical details. In the present study, instead of considering infinitely long-time scale, we aim to provide a framework to understand the long but finite time behavior, namely the transient dynamics. In the analysis, we focus on the Floquet-Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian…
We build a rigorous nonequilibrium thermodynamic description for open chemical reaction networks of elementary reactions. Their dynamics is described by deterministic rate equations satisfying mass action law. Our most general framework considers open networks driven by time-dependent chemostats. The energy and entropy balances are established and a nonequilibrium Gibbs free energy is introduced. The difference between this latter and its equilibrium form represents the minimal work done by the chemostats to bring the network in its nonequilibrium state. It is minimized in nondriven detailed-b…
Numerical simulation of stochastic dynamics of vortex filaments under action of random (Langevin) force is fulfilled. Calculations are performed on base of the full Biot--Savart law for different intensities of the Langevin force. A new algorithm, which is based on consideration of crossing lines, is used for vortex reconnection procedure. After some transient period the vortex tangle develops into the stationary state characterizing by the developed fluctuations of various physical quantities, such as total length, energy etc. We tested this state to learn whether or not it the thermodynamic …
The nature of the behaviour of an isolated many-body quantum system periodically driven in time has been an open question since the beginning of quantum mechanics. After an initial transient, such a system is known to synchronize with the driving; in contrast to the non-driven case, no fundamental principle has been proposed for constructing the resulting non-equilibrium state. Here, we analytically show that, for a class of integrable systems, the relevant ensemble is constructed by maximizing an appropriately defined entropy subject to constraints, which we explicitly identify. This result c…
Finite-Time Thermodynamics of an Autonomous Information Machine
School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）；Key Laboratory of Multiscale Spin Physics (Ministry of Education), Beijing Normal University（北京师范大学多尺度自旋物理教育部重点实验室）
We discuss the role of Bose enhancement of the dipole matrix element in photoassociation, using stimulated Raman adiabatic passage as an example. In a nondegenerate gas the time scale for coherent optical transients tends to infinity in the thermodynamic limit, whereas Bose enhancement keeps this time scale finite in a condensate. Coherent transients are therefore absent in photoassociation of a thermal nondegenerate gas, but are feasible if the gas is a condensate.
A theoretical treatment of deeply supercooled liquids is difficult because their properties emerge from spatial inhomogeneities that are self-induced, transient, and nanoscopic. I use computer simulations to analyse self-induced static and dynamic heterogeneity in equilibrium systems approaching the experimental glass transition. I characterise the broad sample-to-sample fluctuations of salient dynamic and thermodynamic properties in elementary mesoscopic systems. Findings regarding local lifetimes and distributions of dynamic heterogeneity are in excellent agreement with recent single molecul…
We examine the question of whether the formal expressions of equilibrium statistical mechanics can be applied to time independent non-dissipative systems that are not in true thermodynamic equilibrium and are nonergodic. By assuming the phase space may be divided into time independent, locally ergodic domains, we argue that within such domains the relative probabilities of microstates are given by the standard Boltzmann weights. In contrast to previous energy landscape treatments, that have been developed specifically for the glass transition, we do not impose an a priori knowledge of the inte…
We present a generally covariant formulation of conformal higher-order viscoelastic fluid mechanics with strain allowed to take arbitrarily large values. We give a general prescription to determine the dynamics of a relativistic viscoelastic fluid in a way consistent with the hypothesis of local thermodynamic equilibrium and the second law of thermodynamics. We then elaborately study the transient time scales at which the strain almost relaxes and becomes proportional to the gradients of velocity. We particularly show that a conformal second-order fluid with all possible parameters in the cons…
In this paper, we reveal a general relationship between model simplification and irreversibility based on the model of continuous-time Markov chains with time-scale separation. According to the topological structure of the fast process, we divide the states of the chain into the transient states and the recurrent states. We show that a two-time-scale chain can be simplified to a reduced chain in two different ways: removal of the transient states and aggregation of the recurrent states. Both the two operations will lead to a decrease in the entropy production rate and its adiabatic part and wi…
