Nonequilibrium Free Energy Research Articles

Thermodynamics of the Quantum Mpemba Effect.

We investigate the quantum Mpemba effect from the perspective of nonequilibrium quantum thermodynamics by studying relaxation dynamics of quantum systems coupled to a Markovian heat bath, which are described by Davies maps. Starting from a state with coherences in the energy eigenbasis, we demonstrate that an exponential speedup to equilibrium will always occur if the state is transformed to a diagonal state in the energy eigenbasis, provided that the spectral gap of the generator is defined by a complex eigenvalue. When the transformed state has a higher nonequilibrium free energy, we argue using thermodynamic reasoning that this is a genuine quantum Mpemba effect. Furthermore, we show how a unitary transformation on an initial state can always be constructed to yield the effect and demonstrate our findings by studying the dynamics of both the nonequilibrium free energy and the irreversible entropy production in single and multiqubit examples.

Nonequilibrium dissolution behaviors and mass-transfer parameters for a CO2/heavy-oil system

CO2 nonequilibrium dissolution in heavy oil was thoroughly studied, and the relevant mass-transfer parameters were determined. Experiments were conducted at different scales, including a single ultrathin microfluidic channel and ultrathin bulk-phase cell. A continuum-scale simulator coupled with an external real-time programing command was developed to determine the mass-transfer parameters, including the intraphase effective diffusion coefficients and interphase nonequilibrium mass-transfer rates. The former were correlated with the solvent concentration and chemical potential of the system, while the latter were calculated using nonequilibrium chemical potential decay, which was correlated with the system pressure and free energy. The newly developed simulator was verified using literature data from various experimental scales, including PVT cells and microfluidics. The simulator incorporates the effect of nonequilibrium free energy on interphase mass transfer in quiescent molecular diffusion-dominated processes, providing a viable technique for accurately simulating continuum-scale mass transfer, particularly in solvent-based injection.

Bidirectional path-based non-equilibrium simulations for binding free energy

Estimating free energy is a fundamental computational challenge, especially in complex biological systems characterised by numerous degrees of freedom. In this study, we investigate the potential of leveraging non-equilibrium free energy estimators within path-based approaches; this offers an appealing feature of inherent parallelism. Building upon our prior work on protein-ligand binding free energy calculations, we develop its non-equilibrium counterpart. We begin by validating our computational strategy on a simple toy model and then extend our analysis to the well-established trypsin-benzamidine complex, serving as a benchmark system. Subsequently, we apply this method to a more intricate, relevant pharmaceutical system to evaluate the performance of our computational pipeline on this complex system. Our results not only demonstrate the feasibility of this approach but also shed light on potential limitations. Furthermore, we showcase the capabilities of the Jarzynski and Crooks estimators employed in our study.

Growth-induced stability in modified SLE curve

In this study, the non-equilibrium free energy corresponding to the curve generated by a modified stochastic Loewner evolution (SLE), which is driven by the Langevin equation, is theoretically investigated. Under certain conditions, we prove that the time derivative of the (generalized) free energy expressed by Kullback-Leibler divergence between the probability distributions of the curve and driving function has a positive value, indicating the negativity of Gibbs entropy production. In addition, it was implied that, in a certain restriction, the free energy can be expressed as a function of a Lyapunov-type exponent of the driving function. These results show a dissipative nature of conformal dynamics, and indicate the growth-induced stability of the modified SLE curve.

Optimization of nonequilibrium free energy harvesting illustrated on bacteriorhodopsin

Optimization of nonequilibrium free energy harvesting illustrated on bacteriorhodopsin

Thermodynamic Insights into Symmetry Breaking: Exploring Energy Dissipation across Diverse Scales.

Symmetry breaking is a phenomenon that is observed in various contexts, from the early universe to complex organisms, and it is considered a key puzzle in understanding the emergence of life. The importance of this phenomenon is underscored by the prevalence of enantiomeric amino acids and proteins.The presence of enantiomeric amino acids and proteins highlights its critical role. However, the origin of symmetry breaking has yet to be comprehensively explained, particularly from an energetic standpoint. This article explores a novel approach by considering energy dissipation, specifically lost free energy, as a crucial factor in elucidating symmetry breaking. By conducting a comprehensive thermodynamic analysis applicable across scales, ranging from elementary particles to aggregated structures such as crystals, we present experimental evidence establishing a direct link between nonequilibrium free energy and energy dissipation during the formation of the structures. Results emphasize the pivotal role of energy dissipation, not only as an outcome but as the trigger for symmetry breaking. This insight suggests that understanding the origins of complex systems, from cells to living beings and the universe itself, requires a lens focused on nonequilibrium processes.

Catalysis in action via elementary thermal operations

We investigate catalysis in the framework of elementary thermal operations (ETOs), leveraging the distinct features of such operations to illuminate catalytic dynamics. As groundwork, we establish new technical tools that enhance the computability of state transition rules for ETOs. Specifically, we provide a complete characterisation of state transitions for a qutrit system and special classes of initial states of arbitrary dimension. By employing these tools in conjunction with numerical methods, we find that by adopting a small catalyst, including just a qubit catalyst, one can significantly enlarge the set of state transitions for a qutrit system. This advancement notably narrows the gap of reachable states between ETOs and generic thermal operations. Furthermore, we decompose catalytic transitions into time-resolved evolution, which critically enables the tracking of nonequilibrium free energy exchanges between the system and bath. Our results provide evidence for the existence of simple and practicable catalytic advantage in thermodynamics while offering insight into analysing the mechanism of catalytic processes.

Quantum non-Markovianity, quantum coherence and extractable work in a general quantum process.

A key concept in quantum thermodynamics is extractable work, which specifies the maximum amount of work that can be extracted from a quantum system. Different quantities are used to measure extractable work, the most prevalent of which are ergotropy and the difference between the non-equilibrium and equilibrium quantum free energies. Using the latter, we investigate the evolution of extractable work when an open quantum system undergoes a general quantum process described by a completely-positive and trace-preserving dynamical map. We derive a fundamental equation of thermodynamics for such processes as a relation between the distinct sorts of energy change in such a way that the first and the second law of thermodynamics are combined. We then identify the contributions from the reversible and irreversible processes in this equation and demonstrate that they are respectively responsible for the evolution of heat and extractable work of the open quantum system. Furthermore, we show how this correspondence between irreversibility and extractable work has the potential to provide a clear explanation of how the quantum properties of a system affect its extractable work evolution. Specifically, we establish this by directly connecting the change in extractable work with the change in standard quantifiers of quantum non-Markovianity and quantum coherence during a general quantum process. We illustrate these results with two examples.

An anisotropic finite strain elastoplastic model considering different plastic spin effects on the intermediate configuration

Large deformation anisotropic elastoplastic models have important application background and research value in engineering and materials fields. In this paper, a macroscopic phenomenological model of elastoplastic anisotropic deformation considering plastic spin is proposed. The model is based on the multiplication decomposition of deformation gradient. The free energy function is expressed as the isotropic function of the strain and the structural tensor on the intermediate configuration, which is a push-forward of initial configuration by using plastic deformation gradient. Advantageously, the non-equilibrium free energy function remains invariant under the superimposed rigid body rotation on the intermediate configuration, which is due to the non-uniqueness of the multiplicative decomposition of deformation gradient. However, the rate of superimposed rigid body rotation has effects on the model. The effects are discussed by considering three different spin assumptions. Numerical simulations show that the plastic spin has influence on the calculation results. Therefore, the plastic spin assumption should be carefully selected in the practical application of elastoplastic anisotropic model.

Noise-to-energy conversion in a nanometer-scale dot observed with electron counting statistics

We converted Gaussian-distributed voltage noise applied to an electron reservoir into the non-equilibrium free energy of a nanometer-scale dot connected to the reservoir via an energy barrier. Counting statistics of single-electron motion into and out of the dot through the energy barrier allows us to quantitatively analyze the energy transported into the dot as well as changes in the internal energy and effective temperature of the dot in this noise-induced non-equilibrium steady state (NESS). By analyzing the transition rates of electrons moving into and out of the dot, we confirmed that the rectification effect caused by the asymmetry with respect to the direction of electron motion is the origin of the increase in the internal energy of the dot. The information on energy transport in a nanometer-scale dot in the noise-induced NESS obtained in this study with electron counting statistics clarifies the relationship between the non-equilibrium dynamics of a nanodevice and noise applied to it. This study provides us with the means to evaluate device operation using noise as a resource.

Thermal divergences of quantum measurement engine

A quantum engine fueled by quantum measurement is proposed. Under the finite-time unitary transformation, the conversion of heat to work is realized without the compression and expansion of the resonance frequency. The work output, quantum heat, and efficiency are derived, highlighting the important role of the thermal divergence recently reappearing in open quantum systems. The key problem of how the measurement basis can be optimized to enhance the performance is solved by connecting the thermal divergence to the nonequilibrium free energy and entropy. The spin-engine architecture offers a comprehensive platform for future investigations of extracting work from quantum measurement.

Non-equilibrium early-warning signals for critical transitions in ecological systems

Complex systems can exhibit sudden transitions or regime shifts from one stable state to another, typically referred to as critical transitions. It becomes a great challenge to identify a robust warning sufficiently early that action can be taken to avert a regime shift. We employ landscape-flux theory from nonequilibrium statistical mechanics as a general framework to quantify the global stability of ecological systems and provide warning signals for critical transitions. We quantify the average flux as the nonequilibrium driving force and the dynamical origin of the nonequilibrium transition while the entropy production rate as the nonequilibrium thermodynamic cost and thermodynamic origin of the nonequilibrium transition. Average flux, entropy production, nonequilibrium free energy, and time irreversibility quantified by the difference in cross-correlation functions forward and backward in time can serve as early warning signals for critical transitions much earlier than other conventional predictors. We utilize a classical shallow lake model as an exemplar for our early warning prediction. Our proposed method is general and can be readily applied to assess the resilience of many other ecological systems. The early warning signals proposed here can potentially predict critical transitions earlier than established methods and perhaps even sufficiently early to avert catastrophic shifts.

Roles of local nonequilibrium free energy in the description of biomolecules.

When a system is in equilibrium, external perturbations yield a time series of nonequilibrium distributions, and recent experimental techniques give access to the nonequilibrium data that may contain critical information. Jinwoo and Tanaka [Sci. Rep. 5, 7832 (2015)2045-232210.1038/srep07832] have provided mathematical proof that such a process's nonequilibrium free energy profile over a system's substates has Jarzynski's work as content, which spontaneously dissipates while molecules perform their tasks. Here we numerically verify this fact and give a practical example where we analyze a computer simulation of RNA translocation by a ring-shaped ATPase motor. By interpreting the cyclic process of substrate translocation as a series of quenching, relaxation, and second quenching, the theory gives how the ATPase motor allocates the hydrolysis energy between individual substates until the end of the process. It turns out that the efficiency of RNA translocation is 48%-60% for most molecules, but 12% of molecules achieve 80%-100% efficiency, which is consistent with the literature. This theory would be a valuable tool for extracting quantitative information about molecular nonequilibrium behavior from experimental observations.

Hepatoprotective Effect of Millettia dielsiana: In Vitro and In Silico Study.

In silico docking studies of 50 selected compounds from Millettia dielsiana Harms ex Diels (family Leguminosae) were docked into the binding pocket of the PI3K/mTOR protein. In there, compounds trans-3-O-p-hydroxycinnamoyl ursolic acid (1) and 5,7,4'-trihydroxyisoflavone 7-O-β-D-apiofuranosyl-(1→6)-β-D-glucopyranoside (2) are predicted to be very promising inhibitors against PI3K/mTOR. They direct their cytotoxic activity against Hepatocellular carcinoma with binding affinity (BA) values, the pulling work spent to the co-crystallized ligand from the binding site of PI3K/mTOR (W and Fmax), and the non-equilibrium binding free energy (∆GneqJar) as BA values = -9.237 and -9.083 kcal/mol, W = 83.5 ± 10.6 kcal/mol with Fmax = 336.2 ± 45.3 pN and 126.6 ± 21.7 kcal/mol with Fmax = 430.3 ± 84.0 pN, and ∆GneqJar = -69.86074 and -101.2317 kcal/mol, respectively. In molecular dynamic simulation, the RMSD value of the PI3K/mTOR complex with compounds (1 and 2) was in the range of 0.3 nm to the end of the simulation. Therefore, the compounds (1 and 2) are predicted to be very promising inhibitors against PI3K/mTOR. The crude extract, ethyl acetate fraction and compounds (1 and 2) from Millettia dielsiana exhibited moderate to potent in vitro cytotoxicity on Hepatocellular carcinoma cell line with IC50 values of 81.2 µg/mL, 60.4 µg/mL, 23.1 μM, and 16.3 μM, respectively, and showed relatively potent to potent in vitro antioxidant activity on mouse hepatocytes with ED50 values of 24.4 µg/mL, 19.3 µg/mL, 30.7 μM, and 20.5 μM, respectively. In conclusion, Millettia dielsiana and compounds (1 and 2) are predicted to have very promising cytotoxic activity against Hepatocellular carcinoma and have a hepatoprotective effect.

The Boltzmann distribution function for equilibrium fluctuations

A complex of issues related to the problem of proving the Boltzmann formula for the probability density (distribution) w(η) of the values of a certain set of parameters η of an equilibrium system is investigated. The classical Boltzmann formula expresses this distribution through the non-equilibrium free energy of the system F (η) , which depends on the mentioned parameters. This is possible because after the occurrence of fluctuations, the system finds itself in a non-equilibrium state, which evolves further to equilibrium. The specified parameters are chosen according to the problem under consideration. In the theory of phase transitions, they are called the order parameters. Questions under consideration include definition and construction of the free energy F (η) of a non-equilibrium system and distribution w(η ) for it in the microscopic theory. The approaches of Landau, Leontovich, and Peletminsky are discussed. It is proposed to investigate the results for states in the vicinity of equilibrium. The leading ideas of the research are considering the non-equilibrium state as being realized in the presence of an appropriate external field, using the Gibbs formula for the non-equilibrium system entropy, and applying the Boltzmann formula as a definition of the free energy of the non-equilibrium system. The article is a continuation of the authors' works and sets the task of clarifying some of their statements as well as simplifying and clarifying the calculations. Among other things, the following are discussed: the formula for the expansion of the free energy of the system in powers of the field, the simplification of the distribution w(η ) calculation, the normalization of the approximate expressions for the distribution w(η) , the possibilities of studying the free energy of the equilibrium system using our expression for the effective Landau Hamiltonian, the refinement of the calculation of the non-equilibrium free energy of a spatially inhomogeneous system, the investigation of new types of effective interactions with the Landau Hamiltonian.

Extraction of ergotropy: free energy bound and application to open cycle engines

The second law of thermodynamics uses change in free energy of macroscopic systems to set a bound on performed work. Ergotropy plays a similar role in microscopic scenarios, and is defined as the maximum amount of energy that can be extracted from a system by a unitary operation. In this analysis, we quantify how much ergotropy can be induced on a system as a result of system's interaction with a thermal bath, with a perspective of using it as a source of work performed by microscopic machines. We provide the fundamental bound on the amount of ergotropy which can be extracted from environment in this way. The bound is expressed in terms of the non-equilibrium free energy difference and can be saturated in the limit of infinite dimension of the system's Hamiltonian. The ergotropy extraction process leading to this saturation is numerically analyzed for finite dimensional systems. Furthermore, we apply the idea of extraction of ergotropy from environment in a design of a new class of stroke heat engines, which we label open-cycle engines. Efficiency and work production of these machines can be completely optimized for systems of dimensions 2 and 3, and numerical analysis is provided for higher dimensions.

Simple approach to current-induced bond weakening in ballistic conductors

We present a simple, first principles scheme for calculating mechanical properties of nonequilibrium bulk systems assuming an ideal ballistic distribution function for the electronic states described by the external voltage bias. This allows for fast calculations of estimates of the current-induced stresses inside bulk systems carrying a ballistic current. The stress is calculated using the Hellmann-Feynman theorem, and is in agreement with the derivative of the nonequilibrium free energy. We illustrate the theory and present results for one-dimensional (1D) metal chains. We find that the susceptibility of the yield stress to the applied voltage agrees with the ordering of break voltages among the metals found in experiments. In particular, gold is seen to be the most stable under strong current, while aluminum is the least stable.

Extractable work in quantum electromechanics.

Recent experiments have demonstrated the generation of coherent mechanical oscillations in a suspended carbon nanotube, which are driven by an electric current through the device above a certain voltage threshold, in close analogy with a lasing transition. We investigate this phenomenon from the perspective of work extraction, by modeling a nanoelectromechanical device as a quantum flywheel or battery that converts electrical power into stored mechanical energy. We introduce a microscopic model that qualitatively matches the experimental finding, and we compute the Wigner function of the quantum vibrational mode in its nonequilibrium steady state. We characterize the threshold for self-sustained oscillations using two approaches to quantifying work deposition in nonequilibrium quantum thermodynamics: the ergotropy and the nonequilibrium free energy. We find that ergotropy serves as an order parameter for the phonon lasing transition. The framework we employ to describe work extraction is general and widely transferable to other mesoscopic quantum devices.

Probing Factor Xa Protein-Ligand Interactions: Accurate Free Energy Calculations and Experimental Validations of Two Series of High-Affinity Ligands.

The accurate prediction of protein-ligand binding affinity belongs to one of the central goals in computer-based drug design. Molecular dynamics (MD)-based free energy calculations have become increasingly popular in this respect due to their accuracy and solid theoretical basis. Here, we present a combined study which encompasses experimental and computational studies on two series of factor Xa ligands, which enclose a broad chemical space including large modifications of the central scaffold. Using this integrated approach, we identified several new ligands with different heterocyclic scaffolds different from the previously identified indole-2-carboxamides that show superior or similar affinity. Furthermore, the so far underexplored terminal alkyne moiety proved to be a suitable non-classical bioisosteric replacement for the higher halogen-π aryl interactions. With this challenging example, we demonstrated the ability of the MD-based non-equilibrium free energy calculation approach for guiding crucial modifications in the lead optimization process, such as scaffold replacement and single-site modifications at molecular interaction hot spots.

Non-equilibrium Stationary Properties of the Boundary Driven Zero-Range Process with Long Jumps

We consider the zero-range process with long jumps and in contact with infinitely many reservoirs in its non-equilibrium stationary state. We derive the hydrostatic limit and the Fick's law, which are a consequence of a relationship between the exclusion process and the zero-range process. We also obtain the large deviation principle for the empirical density, i.e. we compute the non-equilibrium free energy.