arXiv subjects

Nahuel Freitas

Publications and source records attributed to Nahuel Freitas.

32 records · Page 2Linked to original sources

arXiv2021

Reliability and entropy production in non-equilibrium electronic memories

We find the relation between reliability and entropy production in a realistic model of electronic memory (low-power MOS-based SRAM) where logical values are encoded as metastable non-equilibrium states. We employ large deviations techniques to obtain an analytical expression for the bistable quasipotential describing the non-equilibrium steady state and use it to derive an explicit expression bounding the error rate of the memory. Our results go beyond the dominant contribution given by classical instanton theory and provide accurate estimates of the error rate as confirmed by comparison with stochastic simulations. The methods developed can be adapted to study the reliability of broad classes of nonlinear devices subjected to thermal noise.

cond-mat.stat-mech↗

arXiv2021

Linear response in large deviations theory: A method to compute non-equilibrium distributions

We consider thermodynamically consistent autonomous Markov jump processes displaying a macroscopic limit in which the logarithm of the probability distribution is proportional to a scale-independent rate function (i.e., a large deviations principle is satisfied). In order to provide an explicit expression for the probability distribution valid away from equilibrium, we propose a linear response theory performed at the level of the rate function. We show that the first order non-equilibrium contribution to the steady state rate function, $g(x)$, satisfies $u(x)\cdot \nabla g(x) = -β\dot W(x)$ where the vector field $u(x)$ defines the macroscopic deterministic dynamics, and the scalar field $\dot W(x)$ equals the rate at which work is performed on the system in a given state $x$. This equation provides a practical way to determine $g(x)$, significantly outperforms standard linear response theory applied at the level of the probability distribution, and approximates the rate function surprisingly well in some far-from-equilibrium conditions. The method applies to a wealth of physical and chemical systems, that we exemplify by two analytically tractable models - an electrical circuit and an autocatalytic chemical reaction network - both undergoing a non-equilibrium transition from a monostable phase to a bistable phase. Our approach can be easily generalized to transient probabilities and non-autonomous dynamics. Moreover, its recursive application generates a virtual flow in the probability space which allows to determine the steady state rate function arbitrarily far from equilibrium.

cond-mat.stat-mech↗

arXiv2021

Stochastic Thermodynamics of Non-Linear Electronic Circuits: A Realistic Framework for Computing around kT

We present a general formalism for the construction of thermodynamically consistent stochastic models of non-linear electronic circuits. The devices constituting the circuit can have arbitrary I-V curves and may include tunnel junctions, diodes, and MOS transistors in subthreshold operation, among others. We provide a full analysis of the stochastic non-equilibrium thermodynamics of these models, identifying the relevant thermodynamic potentials, characterizing the different contributions to the irreversible entropy production, and obtaining different fluctuation theorems. Our work provides a realistic framework to study thermodynamics of computing with electronic circuits. We demonstrate this point by constructing a stochastic model of a CMOS inverter. We find that a deterministic analysis is only compatible with the assumption of equilibrium fluctuations, and analyze how the non-equilibrium fluctuations induce deviations from its deterministic transfer function. Finally, building on the CMOS inverter, we propose a full-CMOS design for a probabilistic bit (or binary stochastic neuron) exploiting intrinsic noise.

cond-mat.stat-mech↗

arXiv2021

Characterizing autonomous Maxwell demons

We distinguish traditional implementations of autonomous Maxwell demons from related linear devices that were recently proposed, not relying on the notions of measurements and feedback control. In both cases a current seems to flow against its spontaneous direction (imposed, e.g., by a thermal or electric gradient) without external energy intake. However, in the latter case, this current inversion may only be apparent. Even if the currents exchanged between a system and its reservoirs are inverted (by creating additional independent currents between system and demon), this is not enough to conclude that the original current through the system has been inverted. We show that this distinction can be revealed locally by measuring the fluctuations of the system-reservoir currents.

cond-mat.stat-mech↗

arXiv2020

Entanglement generation in quantum thermal machines

We show that in a linear quantum machine, a driven quantum system that evolves while coupled with thermal reservoirs, entanglement between the reservoir modes is unavoidably generated. This phenomenon, which occurs at sufficiently low temperatures and is at the heart of the third law of thermodynamics, is a consequence of a simple process: the transformation of the energy of the driving field into pairs of excitations in the reservoirs. For a driving with frequency $ω_{d}$ we show entanglement exists between environmental modes whose frequencies satisfy the condition $ω_{i} + ω_{j}= ω_{d}$. We show that this entanglement can persist for temperatures that can be significantly higher than the lowest achievable ones with sideband resolved cooling methods.

quant-ph↗

arXiv2020

Heat transport in overdamped quantum systems

We obtain an analytical expression for the heat current between two overdamped quantum oscillators interacting with local thermal baths at different temperatures. The total heat current is split into classical and quantum contributions. We show how to evaluate both contributions by taking advantage of the time scale separation associated with the overdamped regime, and without assuming the usual weak coupling and Markovian approximations. We find that non-trivial quantum corrections survive even when the temperatures are high compared to the frequency scale relevant for the overdamped dynamics of the system.

quant-ph↗

arXiv2020

Stochastic and Quantum Thermodynamics of Driven RLC Networks

We develop a general stochastic thermodynamics of RLC electrical networks built on top of a graph-theoretical representation of the dynamics commonly used by engineers. The network is: open, as it contains resistors and current and voltage sources, nonisothermal as resistors may be at different temperatures, and driven, as circuit elements may be subjected to external parametric driving. The proper description of the heat dissipated in each resistor requires care within the white noise idealization as it depends on the network topology. Our theory provides the basis to design circuits-based thermal machines, as we illustrate by designing a refrigerator using a simple driven circuit. We also derive exact results for the low temperature regime in which the quantum nature of the electrical noise must be taken into account. We do so using a semiclassical approach which can be shown to coincide with a fully quantum treatment of linear circuits for which canonical quantization is possible. We use it to generalize the Landauer-Buttiker formula for energy currents to arbitrary time-dependent driving protocols.

quant-ph↗

arXiv2020

Work statistics across a quantum phase transition

We investigate the statistics of the work performed during a quench across a quantum phase transition using the adiabatic perturbation theory. It is shown that all the cumulants of work exhibit universal scaling behavior analogous to the Kibble-Zurek scaling for the average density of defects. Two kinds of transformations are considered: quenches between two gapped phases in which a critical point is traversed, and quenches that end near the critical point. In contrast to the scaling behavior of the density of defects, the scaling behavior of the work cumulants are shown to be qualitatively different for these two kinds of quenches. However, in both cases the corresponding exponents are fully determined by the dimension of the system and the critical exponents of the transition, as in the traditional Kibble-Zurek mechanism (KZM). Thus, our study deepens our understanding about the nonequilibrium dynamics of a quantum phase transition by revealing the imprint of the KZM on the work statistics.

quant-ph↗

arXiv2019

Cooling to absolute zero: The unattainability principle

The unattainability principle (UP) is an operational formulation of the third law of thermodynamics stating the impossibility to bring a system to its ground state in finite time. In this work, several recent derivations of the UP are presented, with a focus on the set of assumptions and allowed sets of operations under which the UP can be formally derived. First, we discuss derivations allowing for arbitrary unitary evolutions as the set of operations. There the aim is to provide fundamental bounds on the minimal achievable temperature, which are applicable with almost full generality. These bounds show that perfect cooling requires an infinite amount of a given resource -- worst-case work, heat bath's size and dimensionality or non-equilibrium states among others -- which can in turn be argued to imply that an infinite amount of time is required to access those resources. Secondly, we present derivations within a less general set of operations conceived to capture a broad class of currently available experimental settings. In particular, the UP is here derived within a model of linear and driven quantum refrigerators consisting on a network of harmonic oscillators coupled to several reservoirs at different temperatures.

quant-ph↗

arXiv2018

Neural Network Operations and Susuki-Trotter evolution of Neural Network States

It was recently proposed to leverage the representational power of artificial neural networks, in particular Restricted Boltzmann Machines, in order to model complex quantum states of many-body systems [Science, 355(6325), 2017]. States represented in this way, called Neural Network States (NNSs), were shown to display interesting properties like the ability to efficiently capture long-range quantum correlations. However, identifying an optimal neural network representation of a given state might be challenging, and so far this problem has been addressed with stochastic optimization techniques. In this work we explore a different direction. We study how the action of elementary quantum operations modifies NNSs. We parametrize a family of many body quantum operations that can be directly applied to states represented by Unrestricted Boltzmann Machines, by just adding hidden nodes and updating the network parameters. We show that this parametrization contains a set of universal quantum gates, from which it follows that the state prepared by any quantum circuit can be expressed as a Neural Network State with a number of hidden nodes that grows linearly with the number of elementary operations in the circuit. This is a powerful representation theorem (which was recently obtained with different methods) but that is not directly useful, since there is no general and efficient way to extract information from this unrestricted description of quantum states. To circumvent this problem, we propose a step-wise procedure based on the projection of Unrestricted quantum states to Restricted quantum states. In turn, two approximate methods to perform this projection are discussed. In this way, we show that it is in principle possible to approximately optimize or evolve Neural Network States without relying on stochastic methods such as Variational Monte Carlo, which are computationally expensive.

quant-ph↗

arXiv2017

How much can we cool a quantum oscillator? A useful analogy to understand laser cooling as a thermodynamical process

We analyze the lowest achievable temperature for a mechanical oscillator (representing, for example, the motion of a single trapped ion) which is coupled with a driven quantum refrigerator. The refrigerator is composed of a parametrically driven system (which we also consider to be a single oscillator in the simplest case) which is coupled to a reservoir where the energy is dumped. We show that the cooling of the oscillator (that can be achieved due to the resonant transport of its phonon excitations into the environment) is always stopped by a fundamental heating process that is always dominant at sufficiently low temperatures. This process can be described as the non resonant production of excitation pairs. This result is in close analogy with the recent study that showed that pair production is responsible for enforcing the validity of the dynamical version of the third law of thermodynamics (Phys. Rev. E 95, 012146). Interestingly, we relate our model to the usual ones used to describe laser cooling of a single trapped ion and reobtaining the correct limiting temperatures for the limits of resolved and non-resolved sidebands. Our findings (that also serve to estimate the lowest temperatures that can be achieved in a variety of other situations) indicate that the limit for laser cooling can also be associated with non resonant pair production. In fact, as we show, this is the case: The limiting temperature for laser cooling is achieved when the cooling transitions induced by the resonant transport of excitations from the motion into the electromagnetic environment is compensated by the heating transitions induced by the creation of phonon-photon pairs.

quant-ph↗

arXiv2016

Fundamental limits for cooling of linear quantum refrigerators

We study the asymptotic dynamics of arbitrary linear quantum open systems which are periodically driven while coupled with generic bosonic reservoirs. We obtain exact results for the heat flowing into the network, which are valid beyond the usual weak coupling or Markovian approximations. We prove the validity of the dynamical third law of thermodynamics (Nernst unattainability principle), showing that the ultimate limit for cooling is imposed by a fundamental heating mechanism which becomes dominant at low temperatures: the non resonant creation of pairs of excitations in the reservoirs induced by the driving field. This quantum effect, which is missed in the weak coupling approximation, restores the unattainability principle whose validity was recently challenged.

quant-ph↗

arXiv2015

Heat transport through ion crystals

We study the thermodynamical properties of crystals of trapped ions which are laser cooled to two different temperatures in two separate regions. We show that these properties strongly depend on the structure of the ion crystal. Such structure can be changed by varying the trap parameters and undergoes a series of phase transitions from linear to zig-zag or helicoidal configurations. Thus, we show that these systems are ideal candidates to observe and control the transition from anomalous to normal heat transport. All structures behave as `heat superconductors', with a thermal conductivity increasing linearly with system size and a vanishing thermal gradient inside the system. However, zig-zag and helicoidal crystals turn out to be hyper sensitive to disorder having a linear temperature profile and a length independent conductivity. Interestingly, disordered 2D ion crystals are heat insulators. Sensitivity to disorder is much smaller in the 1D case.

quant-ph↗

arXiv2015

New analytic solution for the heat flow through a general harmonic network

We present a new analytic expression for the heat current through a general harmonic network coupled with Ohmic reservoirs. We use a new method that enables us to express the stationary state of the network in terms of the eigenvectors and eigenvalues of a generalized cubic eigenvalue problem. In this way, we obtain exact formulae for the heat current and the local temperature inside the network. Our method does not rely in the usual assumptions of weak coupling to the environments or on the existence of an infinite cutoff in the environmental spectral densities. We use this method to study non-equilibrium processes without the weak coupling and Markovian approximations. As a first application of our method, we revisit the problem of heat conduction in 2D and 3D crystals with binary mass disorder. We complement previous results showing that for small systems the scaling of the heat current with the system size greatly depends on the strength of the interaction between system and reservoirs. This somewhat counter-intuitive result seems not to have been noticed before.

quant-ph↗