arXiv subjects

Marcus V. S. Bonança

Publications and source records attributed to Marcus V. S. Bonança.

30 records · Page 2Linked to original sources

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↗

arXiv2019

Approaching Carnot efficiency at maximum power in linear response regime

We construct an example of heat engine whose efficiency at maximum power breaks down the previously derived bounds in the linear response regime. Such example takes a classical harmonic oscillator as the working substance undergoing a finite-time Otto cycle. Using a specific kind of shortcut to adiabaticity, valid only in the linear response regime, quasistatic work is performed at arbitrarily short times. The cycle duration is then reduced to the sum of relaxation times during the thermalization strokes exclusively. Thus, power is maximum since the work is maximum (quasistatic work) and the cycle duration is minimum. Efficiency at maximum power can be made arbitrarily close to Carnot efficiency with an appropriate choice of the ratio between the temperatures of the two heat baths.

cond-mat.stat-mech↗

arXiv2019

Energy extraction of a chaotic system in a cyclic process: a Szilárd Engine perspective

Inspired by the available examples of Microcanonical Szilárd Engines and by the original Szilárd Engine, we devise a system with two degrees of freedom whose ensemble average energy, starting with a microcanical ensemble, decreases after a cyclic variation of its external parameters. We use the Ergodic Adiabatic Theorem to motivate our cycle and numerical simulations to check the decrement in the average energy. We then compare our system to the aforementioned Szilárd Engines, Microcanonical or not, and speculate about symmetry breaking being the cause of energy extraction in cyclic processes, even when non-integrability and chaos are present.

cond-mat.stat-mech↗

arXiv2018

Minimal dissipation in processes far from equilibrium

A central goal of thermodynamics is to identify optimal processes during which the least amount of energy is dissipated into the environment. Generally, even for simple systems, such as the parametric harmonic oscillator, optimal control strategies are mathematically involved, and contain peculiar and counter-intuitive features. We show that optimal driving protocols determined by means of linear response theory exhibit the same step and $δ$-peak like structures that were previously found from solving the full optimal control problem. However, our method is significantly less involved, since only a minimum of a quadratic form has to be determined. In addition, our findings suggest that optimal protocols from linear response theory are applicable far outside their actual range of validity.

cond-mat.stat-mech↗

arXiv2017

Microcanonical Szilárd engines beyond the quasistatic regime

We discuss the possibility of extracting energy from a single thermal bath using microcanonical Szilárd engines operating in finite time. This extends previous works on the topic which are restricted to the quasistatic regime. The feedback protocol is implemented based on linear response predictions of the excess work. It is claimed that the underlying mechanism leading to energy extraction does not violate Liouville's theorem and preserves ergodicity throughout the cycle. We illustrate our results with several examples including an exactly solvable model.

cond-mat.stat-mech↗

arXiv2016

Conditional reversibility in nonequilibrium stochastic systems

For discrete-state stochastic systems obeying Markovian dynamics, we establish the counterpart of the conditional reversibility theorem obtained by Gallavotti for deterministic systems [Ann. de l'Institut Henri Poincaré (A) 70, 429 (1999)]. Our result states that stochastic trajectories conditioned on opposite values of entropy production are related by time reversal, in the long-time limit. In other words, the probability of observing a particular sequence of events, given a long trajectory with a specified entropy production rate $σ$, is the same as the probability of observing the time-reversed sequence of events, given a trajectory conditioned on the opposite entropy production, $-σ$, where both trajectories are sampled from the same underlying Markov process. To obtain our result, we use an equivalence between conditioned ("microcanonical") and biased ("canonical") ensembles of nonequilibrium trajectories. We provide an example to illustrate our findings.

cond-mat.stat-mech↗

arXiv2015

Shortcuts to adiabaticity from linear response theory

A shortcut to adiabaticity is a finite-time process that produces the same final state as would result from infinitely slow driving. We show that such shortcuts can be found for weak perturbations from linear response theory. With the help of phenomenological response functions a simple expression for the excess work is found -- quantifying the nonequilibrium excitations. For two specific examples, the quantum parametric oscillator and the spin-1/2 in a time-dependent magnetic field, we show that finite-time zeros of the excess work indicate the existence of shortcuts. Finally, we propose a degenerate family of protocols, which facilitate shortcuts to adiabaticity for specific and very short driving times.

cond-mat.stat-mech↗

arXiv2015

Degenerate optimal paths in thermally isolated systems

We present an analysis of the work performed on a system of interest that is kept thermally isolated during the switching of a control parameter. We show that there exists, for a certain class of systems, a finite-time family of switching protocols for which the work is equal to the quasistatic value. These optimal paths are obtained within linear response for systems initially prepared in a canonical distribution. According to our approach, such protocols are composed of a linear part plus a function which is odd with respect to time reversal. For systems with one degree of freedom, we claim that these optimal paths may also lead to the conservation of the corresponding adiabatic invariant. This points to an interesting connection between work and the conservation of the volume enclosed by the energy shell. To illustrate our findings, we solve analytically the harmonic oscillator and present numerical results for certain anharmonic examples.

cond-mat.stat-mech↗

arXiv2014

Optimal driving of isothermal processes close to equilibrium

We investigate how to minimize the work dissipated during nonequilibrium processes. To this end, we employ methods from linear response theory to describe slowly varying processes, i.e., processes operating within the linear regime around quasistatic driving. As a main result we find that the irreversible work can be written as a functional that depends only on the correlation time and the fluctuations of the generalized force conjugated to the driving parameter. To deepen the physical insight of our approach we discuss various self-consistent expressions for the response function, and derive the correlation time in closed form. Finally, our findings are illustrated with several analytically solvable examples.

cond-mat.stat-mech↗

arXiv2012

Relaxation in finite and isolated classical systems: an extension of Onsager's regression hypothesis

In order to derive the reciprocity relations, Onsager formulated a relation between thermal equilibrium fluctuations and relaxation widely known as regression hypothesis. It is shown in the present work how such relation can be extended to finite and isolated classical systems. This extension is derived from the fluctuation-dissipation theorem for the microcanonical ensemble. The results are exemplified with a nonintegrable system in order to motivate possible applications to dynamical systems and statistical mechanics of finite systems.

cond-mat.stat-mech↗

arXiv2011

Lyapunov Decoherence Rate in Classically Chaotic Systems

We provide a path integral treatment of the decoherence process induced by a heat bath on a single particle whose dynamics is classically chaotic and show that the decoherence rate is given by the Lyapunov exponent. The loss of coherence is charaterized by the purity, which is calculated semiclassically within diagonal approximation, when the particle initial state is a single gaussian wave packet. The calculation is performed for weak dissipation and in the high temperature limit. This situation allows us to simplify the heat bath description to a single random potential. Although the dissipative term is neglected in such approach, the fluctuating one can be treated phenomenologically to fit with the above regime. Our results are therefore valid for times shorter than the inverse of the dissipation rate.

quant-ph↗

arXiv2008

Fluctuation-Dissipation Theorem for the Microcanonical Ensemble

A derivation of the Fluctuation-Dissipation Theorem for the microcanonical ensemble is presented using linear response theory. The theorem is stated as a relation between the frequency spectra of the symmetric correlation and response functions. When the system is not in the thermodinamic limit, this result can be viewed as an extension of the fluctuation-dissipation relations to a situation where dynamical fluctuations determine the response. Therefore, the relation presented here between equilibrium fluctuations and response can have a very different physical nature from the usual one in the canonical ensemble. These considerations imply that the Fluctuation-Dissipation Theorem is not restricted to the context of thermal equilibrium, where it is usually derived. Dispersion relations and sum rules are also obtained and discussed in the present case. Although analogous to the Kramers-Kronig relations, they are not related to the frequency spectrum but to the energy dependence of the response function.

cond-mat.stat-mech↗