arXiv subjects

Pierre Nazé

Publications and source records attributed to Pierre Nazé.

33 records · Page 2Linked to original sources

arXiv2023

Optimal work fluctuations for thermally isolated systems in weak processes

The fluctuation-dissipation relation for the classical definition of work is extended to thermally isolated systems, in classical and quantum realms. From this, the optimal work variance is calculated, showing it achieves its minimum possible value, independent of the rate of the process, in a so-called quasistatic variance, related to the difference between the quasistatic work and the difference of Helmholtz's free energy of the system. The result is corroborated by the example of the classical and driven harmonic oscillator, whose probability density function of the work distribution is non-Gaussian and constant for different rates. The optimal variance is calculated for the quantum Ising chain as well, showing its finiteness if the linear response validity criterion is complied with. A stronger definition of the arbitrary constant for the relaxation function of thermally isolated systems is obtained along the work.

cond-mat.stat-mech↗

arXiv2023

Probability distribution of classical observables

In this work, I derive the time-dependent probability density function of classical observables using the Hamiltonian mechanics approach, extending the notion of fluctuation theorems for any observables. In particular, the time-dependent probability density function of the thermodynamic work evolving in the switching time is solved as a special case. From such a relation, I prove Jarzynski's equality and Crook's fluctuation theorem. The particular case of a Gaussian distribution for slowly-varying processes is derived as well at the end.

cond-mat.stat-mech↗

arXiv2023

Nonlinear response of the irreversible work via generalized relaxation functions

The nonlinear response of the excess work, when made via series expansion in the parameter perturbation of the average thermodynamic work, requires adjustments to agree with the Second Law of Thermodynamics. In this work, I present a well-behaved nonlinear response of the irreversible work, based on its well-known cumulant series expansion. From the generalization of the fluctuation-dissipation relation derived from it, I define the terms of the series expansion in the parameter perturbation of the irreversible work by the terms of the cumulants. Since every cumulant depends on raw moments, I define from them the generalized relaxation functions, whose arbitrary constants were chosen guaranteeing the accomplishment of the Second Law of Thermodynamics. A procedure to calculate the nonlinear response of the irreversible work is then provided.

cond-mat.stat-mech↗

arXiv2023

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 procedure 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 non-monotonic and rapid protocols.

cond-mat.stat-mech↗

arXiv2023

Time-averaged quantum annealing for weak processes

The quantum Ising chain has shortcuts to adiabaticity when operated with weak processes. However, when exactly do the non-equilibrium effects of the Kibble-Zurek mechanism, inherent to the system, appear in the optimal protocols in such a context? I propose here that such contrasting difference occurs due to the manner by which one measures the excitation spent energy of the system. Therefore, in this work, I made a qualitative analysis of a quantum annealing procedure of the time-averaged excess work, where the system acquires as a diverging decorrelation time the heuristic Kibble-Zurek mechanism relaxation time. Four important effects are then observed: the absence of shortcuts to adiabaticity, the pausing effect around the critical point in the optimal protocol when the Kibble-Zurek mechanism holds, the persistence of the time-averaged work to avoid slowly-varying regime even for large switching times, and diverging fluctuations of the time-averaged work. In the end, by comparing the excess and the time-averaged excess works, I conclude that this last one is not useful to measure the excitation spent energy in weak processes, although brings an intuition to what happens in the strong driving case.

quant-ph↗

arXiv2023

Global optimization and monotonicity in entropy production of weak drivings

Knowing if an optimal solution is local or global has always been a hard question to answer in more sophisticated situations of optimization problems. In this work, for finite-time and weak isothermal driving processes, we show the existence of a global optimal protocol for the entropy production. We prove that by showing its convexity as a functional in the derivative of the protocol. This property also proves its monotonicity in such a context, which leads to the satisfaction of the Second Law of Thermodynamics. In the end, we exemplify that the analytical technique of the Euler-Lagrange equation applied to overdamped Brownian motion delivers the global optimal protocol, by comparing it with the results of the global optimization technique of genetic programming.

cond-mat.stat-mech↗

arXiv2022

Optimal finite-time processes in weakly driven overdamped Brownian motion

The complete physical understanding of the optimization of the thermodynamic work still is an important open problem in stochastic thermodynamics. We address this issue using the Hamiltonian approach of linear response theory in finite time and weak processes. We derive the Euler-Lagrange equation associated and discuss its main features, illustrating them using the paradigmatic example of driven Brownian motion in overdamped regime. We show that the optimal protocols obtained either coincide, in the appropriate limit, with the exact solutions by stochastic thermodynamics or can be even identical to them, presenting the well-known jumps. However, our approach reveals that jumps at the extremities of the process are a good optimization strategy in the regime of fast but weak processes for any driven system. Additionally, we show that fast-but-weak optimal protocols are time-reversal symmetric, a property that has until now remained hidden in the exact solutions far from equilibrium.

cond-mat.stat-mech↗

arXiv2022

Assessing the performance of quantum annealing with nonlinear driving

Current generation quantum annealers have already proven to be successful problem-solvers. Yet, quantum annealing is still very much in its infancy, with suboptimal applicability. For instance, to date it is still an open question which annealing protocol causes the fewest diabatic excitations for a given eigenspectrum, and even whether there is a universally optimal strategy. Therefore, in this paper, we report analytical and numerical studies of the diabatic excitations arising from nonlinear protocols applied to the transverse field Ising chain, the exactly solvable model that serves as a quantum annealing playground. Our analysis focuses on several driving schemes that inhibit or facilitate the dynamic phases discussed in a previous work. Rather remarkably, we find that the paradigmatic Kibble-Zurek behavior can be suppressed with ``pauses'' in the evolution, both for crossing and for stopping at the quantum critical point of the system.

quant-ph↗

arXiv2022

The three phases of quantum annealing: fast, slow, and very slow

Currently, existing quantum annealers have proven themselves as viable technology for the first practical applications in the noisy-intermediate-scale-quantum era. However, to fully exploit their capabilities, a comprehensive characterization of their finite-time excitations is instrumental. To this end, we develop a phase diagram for driven Ising chains, from which the scaling behavior of the excess work can be read off as a function of process duration and system size. "Fast" processes are well described by the Kibble-Zurek mechanism; "slow" processes are governed by effective Landau-Zener dynamics; and "very slow" processes can be approximated with adiabatic perturbation theory.

quant-ph↗

arXiv2022

Kibble-Zurek scaling from linear response theory

While quantum phase transitions share many characteristics with thermodynamic phase transitions, they are also markedly different as they occur at zero temperature. Hence, it is not immediately clear whether tools and frameworks that capture the properties of thermodynamic phase transitions also apply in the quantum case. Concerning the crossing of thermodynamic critical points and describing its non-equilibrium dynamics, the Kibble-Zurek mechanism and linear response theory have been demonstrated to be among the very successful approaches. In the present work, we show that these two approaches are consistent also in the description of quantum phase transitions, and that linear response theory can even inform arguments of the Kibble-Zurek mechanism. In particular, we show that the relaxation time provided by linear response theory gives a rigorous argument for why to identify the "gap" as a relaxation rate, and we verify that the excess work computed from linear response theory exhibits Kibble-Zurek scaling.

cond-mat.stat-mech↗

arXiv2022

Series expansion of the excess work using nonlinear response theory

The calculation of observable averages in non-equilibrium regimes is one of the most important problems in statistical physics. Using the Hamiltonian approach of nonlinear response theory, we obtain a series expansion of the average excess work and illustrate it with specific examples of thermally isolated systems. We report the emergence of non-vanishing contributions for large switching times when the system is subjected to strong driving. The problem is solved by using an adapted multiple-scale method to suppress these secular terms. Our paradigmatic examples show how the method is implemented generating a truncated series that obeys the Second Law of Thermodynamics.

cond-mat.stat-mech↗

arXiv2020

Negative entropy production rates in Drude-Sommerfeld metals

It is a commonly accepted creed that in typical situations the rate of entropy production is non-negative. We show that this assertion is not entirely correct 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.

cond-mat.stat-mech↗

arXiv2020

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; 3. Positive entropy production rate. Our analysis focus 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.

cond-mat.stat-mech↗

arXiv2018

From Weakly Chaotic Dynamics to Deterministic Subdiffusion via Copula Modeling

Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this technique to connect the statistical distributions of weakly chaotic dynamics and deterministic subdiffusion. More precisely, we decompose the jumps distribution of Geisel-Thomae map into a bivariate one and determine the marginal and copula distributions respectively by infinite ergodic theory and statistical inference techniques. We verify therefore that the characteristic tail distribution of subdiffusion is an extreme value copula coupling Mittag-Leffler distributions. We also present a method to calculate the exact copula and joint distributions in the case where weakly chaotic dynamics and deterministic subdiffusion statistical distributions are already known. Numerical simulations and consistency with the dynamical aspects of the map support our results.

physics.data-an↗

arXiv2014

Number of first-passage times as a measurement of information for weakly chaotic systems

We consider a general class of maps of the interval having Lyapunov subexponential instability $|δx_{t}|\sim|δx_{0}|\exp[Λ_{t}(x_{0})ζ(t)]$, where $ζ(t)$ grows sublinearly as $t\rightarrow\infty$. We outline here a scheme [J. Stat. Phys. {\bf 154}, 988 (2014)] whereby the choice of a characteristic function automatically defines the map equation and corresponding growth rate $ζ(t)$. This matching approach is based on the infinite measure property of such systems. We show that the average information that is necessary to record without ambiguity a trajectory of the system tends to $\langleΛ\rangleζ(t)$, suitably extending the Kolmogorov-Sinai entropy and Pesin's identity. For such systems, information behaves like a random variable for random initial conditions, its statistics obeying a universal Mittag-Leffler law. We show that, for individual trajectories, information can be accurately inferred by the number of first-passage times through a given turbulent phase space cell. This enables us to calculate far more efficiently Lyapunov exponents for such systems. Lastly, we also show that the usual renewal description of jumps to the turbulent cell, usually employed in the literature, does not provide the real number of entrances there. Our results are supported by exhaustive numerical simulations.

nlin.CD↗