Irreversible Work Research Articles

Nonequilibrium quantum thermodynamics of determinantal many-body systems: Application to the Tonks-Girardeau and ideal Fermi gases

We develop a general approach for calculating the characteristic function of the work distribution of quantum many-body systems in a time-varying potential, whose many-body wave function can be cast in the Slater determinant form. Our results are applicable to a wide range of systems including an ideal gas of spinless fermions in one dimension (1D), the Tonks-Girardeau (TG) gas of hard-core bosons, as well as a 1D gas of hard-core anyons. In order to illustrate the utility of our approach, we focus on the TG gas confined to an arbitrary time-dependent trapping potential. In particular, we use the determinant representation of the many-body wave function to characterize the nonequilibrium thermodynamics of the TG gas and obtain exact and computationally tractable expressions---in terms of Fredholm determinants---for the mean work, the work probability distribution function, the nonadiabaticity parameter, and the Loschmidt amplitude. When applied to a harmonically trapped TG gas, our results for the mean work and the nonadiabaticity parameter reduce to those derived previously using an alternative approach. We next propose to use periodic modulation of the trap frequency in order to drive the system to highly non-equilibrium states by taking advantage of the phenomenon of parametric resonance. Under such driving protocol, the nonadiabaticity parameter may reach large values, which indicates a large amount of irreversible work being done on the system as compared to sudden quench protocols considered previously. This scenario is realizable in ultracold atom experiments, aiding fundamental understanding of all thermodynamic properties of the system.

Quantum coherence and criticality in irreversible work

The irreversible work during a driving protocol constitutes one of the most widely studied measures in non-equilibrium thermodynamics, as it constitutes a proxy for entropy production. In quantum systems, it has been shown that the irreversible work has an additional, genuinely quantum mechanical contribution, due to coherence produced by the driving protocol. The goal of this paper is to explore this contribution in systems that undergo a quantum phase transition. Substantial effort has been dedicated in recent years to understand the role of quantum criticality in work protocols. However, practically nothing is known about how coherence contributes to it. To shed light on this issue, we study the entropy production in infinitesimal quenches of the one-dimensional XY model. For quenches in the transverse field, we find that for finite temperatures the contribution from coherence can, in certain cases, account for practically all of the entropy production. At low temperatures, however, the coherence presents a finite cusp at the critical point, whereas the entropy production diverges logarithmically. Alternatively, if the quench is performed in the anisotropy parameter, we find that there are situations where all of the entropy produced is due to quantum coherences.

The Gouy-Stodola Theorem and the derivation of exergy revised

The Gouy-Stodola Theorem is the theoretical basis for allocating irreversibility and for identifying the maximum possible efficiency for any kind of energy conversion system. The well-known theorem is re-obtained in this paper, relaxing the hypothesis about a constant value for temperature and pressure of the reference environment. The equations that have been derived taking into account the variation of reference temperature and pressure show that two additional terms appear in both reversible and irreversible maximum useful work output, besides the well-known terms. These additional terms take into account the potential useful work (exergy) destruction related to the variation of the ambient condition during the considered time interval. In this way the Gouy-Stodola Theorem still holds, but the allocation of exergy destruction is generally different from that calculated in the usual hypothesis of constant temperature and pressure of the reference environment. The Gouy-Stodola Theorem is also used in various textbooks for defining the flow and the non-exergy of a control volume. The same approach is applied in this paper, highlighting the differences and the difficulties related to the variation of the reference pressure and temperature in the reference environment.

Fast-forward approach to stochastic heat engine.

The fast-forward (FF) scheme proposed by Masuda and Nakamura [Proc. R. Soc. A 466, 1135 (2010)1364-502110.1098/rspa.2009.0446] in the context of conservative quantum dynamics can reproduce a quasistatic dynamics in an arbitrarily short time. We apply the FF scheme to the classical stochastic Carnot-like heat engine which is driven by a Brownian particle coupled with a time-dependent harmonic potential and working between the high- (T_{h}) and low- (T_{c}) temperature heat reservoirs. Concentrating on the underdamped case where momentum degree of freedom is included, we find the explicit expressions for the FF protocols necessary to accelerate both the isothermal and thermally adiabatic processes and obtain the reversible and irreversible works. The irreversible work is shown to consist of two terms with one proportional to and the other inversely proportional to the friction coefficient. The optimal value of efficiency η at the maximum power of this engine is found to be η^{*}=1/2{1+1/2(T_{c}/T_{h})^{1/2}-5/4T_{c}/T_{h}+O[(T_{c}/T_{h})^{3/2}]} and η^{*}=1-(T_{c}/T_{h})^{1/2}, respectively, in the cases of strong and weak dissipation. The result is justified for a wide family of time-scaling functions, making the FF protocols very flexible. We also revealed that the accelerated full cycle of the Carnot-like stochastic heat engine cannot be conceivable within the framework of the overdamped case, and the power and efficiency can be evaluated only when the momentum degree of freedom is taken into consideration.

Experimental-numerical failure analysis of the c-Al0.66Ti0.34N-M2 steel system applying instrumented indentation and extended finite element method

An experimental-numerical methodology for failure analysis of the c-Al0.66Ti0.34N/Interface/M2 steel coating system is proposed here. This c-Al0.66Ti0.34N coating was deposited by the arc-PVD technique. The values of the elastic modulus, the fracture energy release rate and the nano-hardness of the coating were obtained by nanoindentation. Normal and shear stress limits of the interface, as well as the adhesive and cohesive critical loads, were measured with the scratch test method. A finite element analysis, using the experimental mechanical properties, was carried out to understand the relationship between the irreversible work vs. depth curve and the mechanical failure evolution of the coating-substrate system, associating the pop-in with nucleation, crack growth and cracking pattern. Extended finite element method (XFEM) was applied for modeling of the mechanical behavior of the coating; the cohesive zones approach was applied for modeling the interface and the Ramberg-Osgood law for modeling the substrate. This approach proposes an experimental-numerical methodology for failure analysis of hard coatings (monolithic body) allowing to calculate fracture energy of the coating material and to model cracking patterns caused by contact mechanics. This work is the first step to answer questions about multi-scale approaches for multi-functional multi-layer coatings to push their enhancements and further applications.

Time-energy uncertainty principle for irreversible heat engines.

Even though irreversibility is one of the major hallmarks of any real-life process, an actual understanding of irreversible processes remains still mostly semi-empirical. In this paper, we formulate a thermodynamic uncertainty principle for irreversible heat engines operating with an ideal gas as a working medium. In particular, we show that the time needed to run through such an irreversible cycle multiplied by the irreversible work lost in the cycle is bounded from below by an irreducible and process-dependent constant that has the dimension of an action. The constant in question depends on a typical scale of the process and becomes comparable to Planck's constant at the length scale of the order Bohr radius, i.e. the scale that corresponds to the smallest distance on which the ideal gas paradigm realistically applies. This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.

Optimization of Stochastic Thermodynamic Machines

The study of stochastic thermodynamic machines is one of the main topics in nonequilibrium thermodynamics. In this study, within the framework of Fokker-Planck equation, and using the method of characteristics of partial differential equation as well as the variational method, performance of stochastic thermodynamic machines is optimized according to the external potential, with the irreversible work $W_{irr}$, or the total entropy production $\Delta S_{\rm tot}$ equivalently, reaching its lower bound. Properties of the optimal thermodynamic machines are discussed, with explicit expressions of upper bounds of work output $W$, power $P$, and energy efficiency $\eta$ are presented. To illustrate the results obtained, typical examples with optimal protocols (external potentials) are also presented.

Evolutions of temperature and density during roll compaction of a pharmaceutical excipient.

Roll compaction is a critical unit operation in the pharmaceutical manufacture. During roll compaction, a change in the internal energy of powder due to applying of external work from the rolls can generate heat and cause an increase in the temperature of the powder, which can subsequently affect the roll compaction behaviour and the quality of ribbons. Thus, it is crucial to understand the thermal response of pharmaceutical formulations during roll compaction. This study hence aims to examine the evolution of temperature and density in powders during roll compaction. For this purpose, a systematic experimental study is performed using the peripheral quantitative computed tomography (PQCT), for the first time, and the thermographic method to investigate the thermo-mechanical behaviour of pharmaceutical powders during roll compaction. A finite element model is also developed to describe the transformation of irreversible compression work to heat as well as the energy dissipation due to the wall friction, and to predict the thermomechanical behaviour. In particular, the effect of roll speeds on the thermomechanical behaviour of powders during roll compaction is examined. It was shown that at low roll speeds, the highest temperature is reached inside of the compacted powder. As the roll speed increases, more heat is generated on the ribbon surfaces due to the powder-wall friction, while the density of ribbon deceases. It was found that the density and the temperature at the ribbon centre, were generally higher than that near to the edge, for roll compaction with fixed cheek plates.

Optimisation of a class of heat engines with explicit solution

A specific class of stochastic heat engines driven cyclically by time-dependent potential, which is defined in the half-line (0<x<+∞), is analysed. For such engines, most of their physical quantities can be obtained explicitly, including the entropy and internal energy of the heat engine, as well as output work (power) and heat exchange with the environment during a finite time interval. The optimisation method based on the external potential to reduce irreversible work and increase energy efficiency is presented. With this optimised potential, efficiency η∗ and its particular value at maximum power ηEMP∗ are calculated and discussed briefly.

Role of coherence in the nonequilibrium thermodynamics of quantum systems.

Exploiting the relative entropy of coherence, we isolate the coherent contribution in the energetics of a driven nonequilibrium quantum system. We prove that a division of the irreversible work can be made into a coherent and incoherent part. This provides an operational criterion for quantifying the coherent contribution in a generic nonequilibrium transformation on a closed quantum system. We then study such a contribution in two physical models of a driven qubit and kicked rotor. In addition, we also show that coherence generation is connected to the nonadiabaticity of a processes, for which it gives the dominant contribution for slow-enough transformations. The amount of generated coherence in the energy eigenbasis is equivalent to the change in diagonal entropy, and here we show that it fulfills a fluctuation theorem.

Quench dynamics and zero-energy modes: The case of the Creutz model

In most lattice models, the closing of a band gap typically occurs at high-symmetry points in the Brillouin zone. Differently, in the Creutz model $-$ describing a system of spinless fermions hopping on a two-leg ladder pierced by a magnetic field $-$ the gap closing at the quantum phase transition between the two topologically nontrivial phases of the model can be moved by tuning the hopping amplitudes. We take advantage of this property to examine the nonequilibrium dynamics of the model after a sudden quench of the magnetic flux through the plaquettes of the ladder. For a quench to one of the equilibrium quantum critical points we find that the revival period of the Loschmidt echo $-$ measuring the overlap between initial and time-evolved states $-$ is controlled by the gap closing zero-energy modes. In particular, and contrary to expectations, the revival period of the Loschmidt echo for a finite ladder does not scale linearly with size but exhibits jumps determined by the presence or absence of zero-energy modes. We further investigate the conditions for the appearance of dynamical quantum phase transitions in the model and find that, for a quench {\em to} an equilibrium critical point, such transitions occur only for ladders of sizes which host zero-energy modes. Exploiting concepts from quantum thermodynamics, we show that the average work and the irreversible work per lattice site exhibit a weak dependence on the size of the system after a quench {\em across} an equilibrium critical point, suggesting that quenching into a different phase induces effective correlations among the particles.

Fast control of interactions in an ultracold two atom system: Managing correlations and irreversibility

We design and explore a shortcut to adiabaticity (STA) for changing the interaction strength between two ultracold, harmonically trapped bosons. Starting from initially uncorrelated, non-interacting particles, we assume a time-dependent tuning of the inter-particle interaction through a Feshbach resonance, such that the two particles are strongly interacting at the end of the driving. The efficiency of the STA is then quantified by examining the thermodynamic properties of the system, such as the irreversible work, which is related to the out-of-equilibrium excitations in the system. We also quantify the entanglement of the two-particle state through the von Neumann entropy and show that the entanglement produced in the STA process matches that of the desired target state. Given the fundamental nature of the two-atom problem in ultracold atomic physics, the presented shortcut can be expected to have significant impact on many processes that rely on inter-particle interactions.

Exergy surface shaping and thermodynamic flow control of electro-mechanical-thermal systems

This paper extends the concepts and tools of Hamiltonian surface shaping and power flow control (HSSPFC) for electro-mechanical (EM) systems to exergy surface shaping and thermodynamic flow control (ESSTFC) for electro-mechanical-thermal (EMT) systems (i.e., irreversible work processes with heat and mass flows). For this paper, extended irreversible thermodynamics will be utilised to produce consistent thermal equations of motion that directly include the exergy destruction terms. A simplified EMT system that models the EMT dynamics of a Navy ship equipped with a railgun is used to demonstrate the application of ESSTFC for designing high performance, stable nonlinear controllers for EMT systems.

Irreversible work reduction by disorder in many-body quantum systems

We study the effect of disorder on work exchange associated to quantum Hamiltonian processes by considering an Ising spin chain in which the strength of coupling between spins are randomly drawn from either Normal or Gamma distributions. The chain is subjected to a quench of the external transverse field which induces this exchange of work. In particular, we study the irreversible work incurred by a quench as a function of the initial temperature, field strength and magnitude of the disorder. While presence of weak disorder generally increases the irreversible work generated, disorder of sufficient strength can instead reduce it, giving rise to a disorder induced lubrication effect. This reduction of irreversible work depends on the nature of the distribution considered, and can either arise from acquiring the behavior of an effectively smaller quench for the Normal-distributed spin couplings, or that of effectively single spin dynamics in the case of Gamma distributed couplings.

Transient Temperature Monitoring of Pharmaceutical Tablets During Compaction Using Infrared Thermography.

Manufacturing of pharmaceutical tablets from powders is always accompanied by the conversion of irreversible mechanical work of compaction into heat. The heat is generated due to friction between powder particles, particles and the die wall, plastic deformation of particles, bonding, and other irreversible processes. The resulting temperature increase potentially might have significant effects on a tablet's mechanical properties, disintegration time, and drug release. In the present work, we show that using infrared thermography as a nondestructive and noncontact process analytical technology (PAT) tool to measure the tablet's rate of cooling, in contrast to the temperature evolution, can be directly related to the tablet's thermal diffusivity. Results show the potential capabilities of this technique to discriminate and toward predicting tensile strength of tablets between same formulations produced at same compaction force but experienced different process shear conditions. Correlation of the tablet's tensile strength, relative density, and rate of cooling at regular regime with respect to different process shear is also discussed.

Two famous results of Einstein derived from the Jarzynski equality

The Jarzynski equality (JE) is a remarkable statement relating transient irreversible processes to infinite-time free energy differences. Although 20 years old, the JE remains unfamiliar to many; nevertheless, it is a robust and powerful law. We examine two of Einstein's most simple and well-known discoveries, one classical and one quantum, and show how each of these follows from the JE. Our first example is Einstein's relation between the drag and diffusion coefficients of a particle in Brownian motion. In this context, we encounter a paradox in the macroscopic limit of the JE which is fascinating but also warns us against using the JE too freely outside of the microscopic domain. Our second example is the equality of Einstein's B coefficients for absorption and stimulated emission of quanta. Here, resonant light does irreversible work on a sample, and the argument differs from Einstein's equilibrium reasoning using the Planck black-body spectrum. We round out our examples with a brief derivation and discussion of Jarzynski's remarkable equality.

An efficient nonlinear Feshbach engine

We investigate a thermodynamic cycle using a Bose–Einstein condensate (BEC) with nonlinear interactions as the working medium. Exploiting Feshbach resonances to change the interaction strength of the BEC allows us to produce work by expanding and compressing the gas. To ensure a large power output from this engine these strokes must be performed on a short timescale, however such non-adiabatic strokes can create irreversible work which degrades the engine’s efficiency. To combat this, we design a shortcut to adiabaticity which can achieve an adiabatic-like evolution within a finite time, therefore significantly reducing the out-of-equilibrium excitations in the BEC. We investigate the effect of the shortcut to adiabaticity on the efficiency and power output of the engine and show that the tunable nonlinearity strength, modulated by Feshbach resonances, serves as a useful tool to enhance the system’s performance.

Thermal effects in landslide mobility

The paper describes a thermo-hydro-mechanical formulation to model thermally induced effects due to the irreversible work input generated during soil deformation. The model was implemented into a material point calculation procedure. The method is applied to the analysis of landslides. A simple slope stability is first analysed. Mechanical work essentially dissipates in shearing bands, which develop excess pore water pressures. The marked effect of soil permeability to control the slide motion after failure is described. Shear band thickness is also a relevant control variable. The problem posed by the non-realistic thickness of shear bands in numerical calculation is addressed by means of a numerical procedure that includes consideration of embedded shear bands where the strains are assumed to be localised. Balance equations describing local flow and thermal interactions between shear bands and the remaining material are formulated. The method is applied to model the instability and subsequent rapid motion of Vajont landslide. Calculated run-out and sliding velocity reproduce, in a satisfactory manner, field observations.

Shortcuts to isothermality and nonequilibrium work relations.

In conventional thermodynamics, it is widely acknowledged that the realization of an isothermal process for a system requires a quasistatic controlling protocol. Here we propose and design a strategy to realize a finite-rate isothermal transition from an equilibrium state to another one at the same temperature, which is named the "shortcut to isothermality." By using shortcuts to isothermality, we derive three nonequilibrium work relations, including an identity between the free-energy difference and the mean work due to the potential of the original system, a Jarzynski-like equality, and the inverse relationship between the dissipated work and the total driving time. We numerically test these three relations by considering the motion of a Brownian particle trapped in a harmonic potential and dragged by a time-dependent force.

Perturbative expansion of irreversible work in Fokker–Planck equation à la quantum mechanics

We discuss the systematic expansion of the solution of the Fokker–Planck equation with the help of the eigenfunctions of the time-dependent Fokker–Planck operator. The expansion parameter is the time derivative of the external parameter which controls the form of an external potential. Our expansion corresponds to the perturbative calculation of the adiabatic motion in quantum mechanics. With this method, we derive a new formula to calculate the irreversible work order by order, which is expressed as the expectation value with a pseudo density matrix. Applying this method to the case of the harmonic potential, we show that the first order term of the expansion gives the exact result. Because we do not need to solve the coupled differential equations of moments, our method simplifies the calculations of various functions such as the fluctuation of the irreversible work per unit time. We further investigate the exact optimized protocol to minimize the irreversible work by calculating its variation with respect to the control parameter itself.