Negative Entropy Production Rate Research Articles

Characterizing the spontaneous collapse of a wavefunction through entropy production

We investigate the phenomenology leading to the non-conservation of energy of the continuous spontaneous localization (CSL) model from the viewpoint of non-equilibrium thermodynamics, and use such framework to assess the equilibration process entailed by the dissipative formulation of the model (dCSL). As a paradigmatic situation currently addressed in frontier experiments aimed at investigating possible collapse theories, we consider a one-dimensional mechanical oscillator in a thermal state. We perform our analysis in the phase space of the oscillator, where the entropy production rate, a non-equilibrium quantity used to characterize irreversibility, can be conveniently analyzed. We show that the CSL model violates Clausius law, as it exhibits a negative entropy production rate, while the dCSL model reaches equilibrium consistently only under certain dynamical conditions, thus allowing us to identify the values—in the parameter space—where the latter mechanism can be faithfully used to describe a thermodynamically consistent phenomenon.

Adiabatic processes like isothermal processes.

The objective of this work is to show that adiabatic processes can be very similar to isothermal ones. First, we show that the criteria for the compatibility of linear-response theory with the second law of thermodynamics for thermally isolated systems are the same as those for systems performing isothermal processes. Motivated by such a result, we explore the thermodynamic consequences of the time-average excess work, observing an unexpected existence of a well-defined relaxation time for thermally isolated systems that obeys the second law of thermodynamics. This is justified by recognizing that such systems, in the usual sense, present random relaxation time, which can be "averaged" by taking the time average of the relaxation function. Such a proceeding is very similar to what happens in isothermal processes, where a stochastic average must be done on the relaxation function to have a well-defined relaxation time. In the end, we analyze the Landau-Zener model from this new point of view, discussing the construction of slowly-varying processes from linear-response theory and observing negative entropy production rates for nonmonotonic and rapid protocols.

Entropy Production in Non-Markovian Collision Models: Information Backflow vs. System-Environment Correlations.

We investigate the irreversible entropy production of a qubit in contact with an environment modelled by a microscopic collision model in both Markovian and non-Markovian regimes. Our main goal is to contribute to the discussions on the relationship between non-Markovian dynamics and negative entropy production rates. We employ two different types of collision models that do or do not keep the correlations established between the system and the incoming environmental particle, while both of them pertain to their non-Markovian nature through information backflow from the environment to the system. We observe that as the former model, where the correlations between the system and environment are preserved, gives rise to negative entropy production rates in the transient dynamics, the latter one always maintains positive rates, even though the convergence to the steady-state value is slower as compared to the corresponding Markovian dynamics. Our results suggest that the mechanism underpinning the negative entropy production rates is not solely non-Markovianity through information backflow, but rather the contribution to it through established system-environment correlations.

Master equation for non-Markovian quantum Brownian motion: The emergence of lateral coherences

Understanding the behavior of a quantum system coupled to its environment is of fundamental interest in the general field of quantum technologies. It also has important repercussions on foundational problems in physics, such as the process of decoherence and the so-called quantum measurement problem. There have been many approaches to explore Markovian and non-Markovian dynamics within the framework of open quantum systems, but the richness of the ensuing dynamics is still not fully understood. In this paper we develop a non-Markovian extension of the standard Caldeira-Leggett model, based on expanding the dynamics of the reduced system at high temperature in inverse powers of the high-frequency cutoff of the Ohmic spectral density of the environment and derive a non-Markovian master equation for the reduced density matrix for the case of a general potential. We also obtain a fully analytical solution in the free particle case. While the short-time behavior of this solution does not diverge substantially from the Markovian behavior, at intermediate times we find a resurgence of coherence, which we name lateral coherence. We identify this with a corresponding transient negative entropy production rate, which is understood to be characteristic of non-Markovian dynamics. We also analyze the positivity of the reduced density matrix and derive the corresponding Fokker-Planck equation in the classical limit.

Negative entropy production rates in Drude-Sommerfeld metals.

It is commonly accepted that in typical situations the rate of entropy production is non-negative. We show that this assertion is not entirely correct, not even in the linear regime, if a time-dependent, external perturbation is not compensated by a rapid enough decay of the response function. This is demonstrated for three variants of the Drude model to describe electrical conduction in noble metals, namely the classical free electron gas, the Drude-Sommerfeld model, and the extended Drude-Sommerfeld model. The analysis is concluded with a discussion of potential experimental verifications and ramifications of negative entropy production rates.

Thermodynamic utility of non-Markovianity from the perspective of resource interconversion

We establish a connection between non-Markovianity and negative entropy production rate for various classes of quantum operations. We analyse several aspects of unital and thermal operations in connection with resource theories of purity and thermodynamics. We fully characterize Lindblad operators corresponding to unital operations. We also characterize the Lindblad dynamics for a large class of thermal operations. We next generalize the definition of the entropy production rate for the non-equilibrium case to connect it with the rate of change of free energy of the system, and establish complementary relations between non-Markovianity and maximum loss of free energy. We naturally conclude that non-Markovianity in terms of divisibility breaking is a necessary resource for the backflow of other resources like purity or free energy under the corresponding allowed operations.

Strong Coupling Thermodynamics of Open Quantum Systems

A general thermodynamic framework is presented for open quantum systems in fixed contact with a thermal reservoir. The first and second law are obtained for arbitrary system-reservoir coupling strengths, and including both factorized and correlated initial conditions. The thermodynamic properties are adapted to the generally strong coupling regime, approaching the ones defined for equilibrium, and their standard weak-coupling counterparts as appropriate limits. Moreover, they can be inferred from measurements involving only system observables. Finally, a thermodynamic signature of non-Markovianity is formulated in the form of a negative entropy production rate.

Compatibility of linear-response theory with the second law of thermodynamics and the emergence of negative entropy production rates

The reliability of physical theories depends on whether they agree with well-established physical laws. In this work, we address the compatibility of the Hamiltonian formulation of linear-response theory with the second law of thermodynamics. In order to do so, we verify three complementary aspects often understood as statements of the second law: (1) no dissipation for quasistatic process; (2) dissipation for finite-time processes; and (3) positive entropy production rate. Our analysis focuses on two classes of nonequilibrium isothermal processes: slowly-varying and finite-time but weak ones. For the former, we show that these aspects are easily verified. For the later, we present conditions for the achievement of the first two aspects. We also show that the third one is not always verified, presenting an example based on Brownian motion in which we observe negative values in the entropy production rate. In particular, we compare linear-response and exact results for this example.

Negative entropy-production rate in Rayleigh-Bénard convection in two-dimensional Yukawa liquids.

The steady-state fluctuation theorem (SSFT) gives the relative probability of occurrence of events violating the second law of thermodynamics in a system with a small number of degrees of freedom. Using two-dimensional complex plasma as a working medium, wherein particle level observation of instantaneous velocities and positions has become experimentally possible, we perform "first-principles" molecular-dynamics simulations using the Yukawa potential in the presence of external gravity and an external temperature gradient leading to the onset and formation of Rayleigh-Bénard convection cells. In such a far-from-equilibrium steady state, the SSFT is put to the test. It is demonstrated that the SSFT is satisfied without any additional fit parameter for observation time τ, comparable to or greater than the relevant microscopic timescale associated with the system under observation.

Non-Markovianity and negative entropy production rates.

Entropy production plays a fundamental role in nonequilibrium thermodynamics to quantify the irreversibility of open systems. Its positivity can be ensured for a wide class of setups, but the entropy production rate can become negative sometimes. This is often taken as an indicator of non-Markovianity. We make this link precise by showing under which conditions a negative entropy production rate implies non-Markovianity and when it does not. For a system coupled to a single heat bath, this can be established within a unified language for two setups: (i) the dynamics resulting from a coarse-grained description of a Markovian master equation and (ii) the classical Hamiltonian dynamics of a system coupled to a bath. The quantum version of the latter result is shown not to hold despite the fact that the integrated thermodynamic description is formally equivalent to the classical case. The instantaneous fixed point of a non-Markovian dynamics plays an important role in our study. Our key contribution is to provide a consistent theoretical framework to study the finite-time thermodynamics of a large class of dynamics with a precise link to its non-Markovianity.

Positive entropy production rate induced by non-Markovianity

The non-Markovian effect on entropy production rate is an open question in quantum thermodynamics. By means of the change rate of the trace distance as the witness, we explore the non-Markovianities for their origin, i.e., from the initial correlation between the system and its heat reservoir and/or from the spectral density of the system-reservoir interaction. We show the possibility of positive entropy production rate regarding the initial correlation, which challenges the existing viewpoint of definitely negative entropy production rate under the non-Markovian condition. Our result is justified by an experimentally feasible model.

Exact master equation for a spin interacting with a spin bath: Non-Markovianity and negative entropy production rate

An exact canonical master equation of the Lindblad form is derived for a central spin interacting uniformly with a sea of completely unpolarized spins. The Kraus operators for the dynamical map are also derived. The non-Markovianity of the dynamics in terms of the divisibility breaking of the dynamical map and increase of the trace distance fidelity between quantum states is shown. Moreover, it is observed that the irreversible entropy production rate is always negative (for a fixed initial state) whenever the dynamics exhibits non-Markovian behavior. In continuation with the study of witnessing non-Markovianity, it is shown that the positive rate of change of the purity of the central qubit is a faithful indicator of the non-Markovian information back flow. Given the experimental feasibility of measuring the purity of a quantum state, a possibility of experimental demonstration of non-Markovianity and the negative irreversible entropy production rate is addressed. This gives the present work considerable practical importance for detecting the non-Markovianity and the negative irreversible entropy production rate.

On Thermodynamics Problems in the Single-Phase-Lagging Heat Conduction Model

Thermodynamics problems for the single-phase-lagging (SPL) model have not been much studied. In this paper, the violation of the second law of thermodynamics by the SPL model is studied from two perspectives, which are the negative entropy production rate and breaking equilibrium spontaneously. The methods for the SPL model to avoid the negative entropy production rate are proposed, which are extended irreversible thermodynamics and the thermal relaxation time. Modifying the entropy production rate positive or zero is not enough to avoid the violation of the second law of thermodynamics for the SPL model, because the SPL model could cause breaking equilibrium spontaneously in some special circumstances. As comparison, it is shown that Fourier’s law and the CV model cannot break equilibrium spontaneously by analyzing mathematical energy integral.

Entropy production of Brownian macromolecules with inertia.

We investigate the nonequilibrium steady-state thermodynamics of single Brownian macromolecules with inertia under feedback control in an isothermal ambient fluid. With the control being represented by a velocity-dependent external force, we find such an open system can have a negative entropy production rate, and we develop a mesoscopic theory consistent with the second law. We propose an equilibrium condition and define a class of external force, which includes the transverse Lorentz force, leading to equilibrium.

Nonviability of some nonlocal electron heat transport modeling

Using exact analytical solutions, it is shown that two recent models of nonlocal electron heat transport are beset with mathematical anomalies leading to unphysical results. First, heat flow with a nonlocal heat flux does not smooth out steep temperature gradients in any finite time. Second, a computation of the thermoelectric field from a vanishing nonlocal current flux is an ill-posed problem leading to instabilities that violate the very assumption on which the model is based. It is verified that these anomalies can lead to a negative entropy production rate, which implies local thermodynamic instability. In particular, it is proved that a temperature distribution that is initially positive can later become negative for certain nonuniform electron density distributions. These results provide a basic understanding of the various difficulties encountered in numerical implementations of these models.

Entropy Production in Oscillating Chemical Systems

Abstract The entropy production in oscillating homogenous chemical systems is investigated by analyzing the difference between the average entropy production rate in a stable periodic oscillatory mode and in the corresponding unstable stationary state. A general analytical expression for this difference in the neighborhood of a Hopf bifurcation is derived. The entropy production in two typical models of chemical systems with unstable stationary states and stable periodic oscillations is investigated, using fixed concentrations as control parameters. The models exemplify both positive and negative entropy production rate differences. One of the investigated models has four free concentrations, the other three. The rate expressions are given by second order mass action kinetics with reverse reactions taken into account. The flows of reactants and products are controlled so that only the free concentrations vary, and the entropy of mixing associated with these flows is discussed.