Nonequilibrium Systems Research Articles

Environment induced dynamical quantum phase transitions in two-qubit Rabi model

Quantum states beyond thermodynamic equilibrium represent fascinating and cutting-edge research. However, the behavior of dynamical quantum phase transitions in complex open quantum systems remains poorly understood. Here, using state-of-the-art numerical approaches, we show that by quenching the qubits-oscillator coupling in a dissipative two-qubit Rabi model, the system undergoes dynamical quantum phase transitions. These transitions are characterized by kinks in the Loschmidt echo rate function at parameter values close to a thermodynamic quantum phase transition and are associated with distinct entanglement features. The two classes of critical phenomena depend on qubit interactions and entanglement, revealing different behaviors of the critical exponent of the first kink of the Loschmidt echo for interacting versus non-interacting qubits. This research enhances our understanding of non-equilibrium quantum systems and offers potential applications in quantum sensing and metrology, as it examines how dynamical transitions can enhance the sensitivity of the Loschmidt echo to the quench parameters.

Speed limits to fluctuation dynamics

Fluctuation dynamics of an experimentally measured observable offer a primary signal for nonequilibrium systems, along with dynamics of the mean. While universal speed limits for the mean have actively been studied recently, constraints for the speed of the fluctuation have been elusive. Here, we develop a theory concerning rigorous limits to the rate of fluctuation growth. We find a principle that the speed of an observable’s fluctuation is upper bounded by the fluctuation of an appropriate observable describing velocity, which also indicates a tradeoff relation between the changes for the mean and fluctuation. We demonstrate the advantages of our inequalities for processes with non-negligible dispersion of observables, quantum work extraction, and the entanglement growth in free fermionic systems. Our results open an avenue toward a quantitative theory of fluctuation dynamics in various non-equilibrium systems encompassing quantum many-body systems and nonlinear population dynamics.

Relaxed hydrodynamic theory of electrically driven nonequilibrium steady states

The capability of hydrodynamics to accurately describe slow and long-wavelength fluctuations around nonequilibrium steady states (NESS), characterized by a stationary flow of energy or matter in the presence of a driving force, remains an open question. In this study, we explicitly construct a hydrodynamic description of electrically driven nonequilibrium charged steady states in the limit in which the relaxation of the first nonhydrodynamic excitation is parametrically slow. Our approach involves introducing gapped modes and extending the effective description into a relaxed hydrodynamic theory (RHT). Leveraging the gauge-gravity duality as a tool for controlled computations within nonequilibrium systems, we establish an ultraviolet complete model for these NESS that confirms the validity of our RHT. In summary, our findings provide a concrete realization of the validity of hydrodynamics beyond thermal equilibrium, offering valuable insights into the dynamics of nonequilibrium systems. Published by the American Physical Society 2024

Intermediate state between steady and breathing solitons in fiber lasers

Ultrafast fiber laser, a vital tool in both science and industry, exhibits two distinct pulse states: the steady soliton (SS) and the breathing soliton (BS). While these states have been extensively studied individually, understanding the complex transition between them is crucial for controlling lasing states effectively. Herein, our experimental observations reveal an intermediate state that toggles between SS and BS, enabled by the dispersive Fourier transform technique. We find that energy hop and decaying breathing processes, driven respectively by the energy quantization effect and Q-switched modulation, govern this transition. Additionally, we observe that the transition between different BS states primarily involves a pure decaying breathing process. Numerical simulations are used to generate similar transition dynamics in a model that combines equations describing the population inversion in a mode-locked laser. This study sheds light on the transition dynamics in non-equilibrium systems, offering insights for intelligently manipulating lasing states.

Dissipation at limited resolutions: power law and detection of hidden dissipative scales

Abstract Non-equilibrium systems, in particular, living organisms, are maintained by irreversible transformations of energy that drive diverse functions. Quantifying their irreversibility, as measured by energy dissipation, is essential for understanding the underlying mechanisms. However, existing techniques usually overlook experimental limitations, either by assuming full information or by employing a coarse-graining method that requires knowledge of the structure behind hidden degrees of freedom. Here, we study the inference of dissipation from finite-resolution measurements by employing a recently developed model-free estimator that considers both the sequence of coarse-grained transitions and the waiting time distributions: σ 2 = σ 2 ℓ + σ 2 t . The dominant term σ 2 ℓ originates from the sequence of observed transitions. We find that it scales with resolution following a power law. Comparing the scaling exponent with a previous estimator highlights the importance of accounting for flux correlations at lower resolutions. σ 2 t comes from asymmetries in waiting time distributions. It is non-monotonic in resolution, with its peak position revealing characteristic scales of the underlying dissipative process, consistent with observations in the actomyosin cortex of starfish oocytes. Alternatively, the characteristic scale can be detected in a crossover of the scaling of σ 2 ℓ . This provides a novel perspective for extracting otherwise hidden characteristic dissipative scales directly from dissipation measurements. We illustrate these results in biochemical models as well as complex networks. Overall, this study highlights the significance of resolution considerations in non-equilibrium systems, providing insight into the interplay between experimental resolution, entropy production and underlying complexity.

New insights into the prediction for the potential of soil organic carbon accumulation: From the perspective of non-equilibrium statistical mechanics

The accumulation of soil organic carbon (SOC) is significant for soil health and ecosystem services. Numerous studies have assessed the dynamic changes of SOC by considering the microbial system as an equilibrium system. However, they failed to reveal the complexity of the SOC accumulation/loss process, as the microbial system is a non-equilibrium system affected by stochastic fluctuations from the external environment. This study is the first to explore the complex non-equilibrium relationship between microbial carbon use efficiency (CUE) and SOC by using potential landscape and flux in non-equilibrium statistical mechanics. Nitrogen (N) was identified as the most critical environmental factor influencing CUE on a global scale, with the transition between the carbon loss state and the carbon sequestration state observed along N gradients. Random perturbations of other environmental factors could also trigger transition. Non-equilibrium thermodynamic quantities indicated that carbon sequestration had the potential to be achieved when N = 0.5 g/kg, where active soil management measures should be taken. Furthermore, the non-equilibrium relationship between CUE and SOC was clarified through potential energy analysis, where the average deviation between predictions and actual observations of SOC is about 1.9792 g/kg. This study provides an effective framework for predicting SOC accumulation.

Nonreciprocal nonlinear responses in moving charge density waves

The incommensurate charge density wave states (CDWs) can exhibit steady motion in the flow limit after depinning, behaving as a nonequilibrium system with time-dependent states. Since the moving CDW, like an electric current, breaks both time-reversal and inversion symmetries, one may speculate the emergence of nonreciprocal nonlinear responses from such motion. However, the moving CDW order parameter is intrinsically time-dependent in the lab frame, and it is known to be challenging to evaluate the responses of such a time-varying system. In this work, following the principle of Galilean relativity, we resolve this time-dependent hard problem in the lab frame by mapping the system to the comoving frame with static CDW states through the Galilean transformation. We explicitly show that the nonreciprocal nonlinear responses would be generated by the movement of CDW states through violating Galilean relativity.

Generalized Itô’s lemma and the stochastic thermodynamics of diffusion with resetting

Abstract Methods from the theory of stochastic processes are increasingly being used to extend classical thermodynamics to mesoscopic non-equilibrium systems. One characteristic feature of these systems is that averaging the stochastic entropy with respect to an ensemble of stochastic trajectories leads to a second law of thermodynamics that quantifies the degree of departure from thermodynamic equilibrium. A well known mechanism for maintaining a diffusing particle out of thermodynamic equilibrium is stochastic resetting. In its simplest form, the position of the particle instantaneously resets to a fixed position x 0 at a sequence of times generated from a Poisson process of constant rate r. Within the context of stochastic thermodynamics, instantaneous resetting to a single point is a unidirectional process that has no time-reversed equivalent. Hence, the average rate of entropy production calculated using the Gibbs–Shannon entropy cannot be related to the degree of time-reversal symmetry breaking. The problem of unidirectionality can be avoided by considering resetting to a random position or diffusion in an intermittent confining potential. In this paper we show how stochastic entropy production along sample paths of diffusion processes with resetting can be analyzed in terms of extensions of Itô’s formula for stochastic differential equations (SDEs) that include both continuous and discrete processes. First, we use the stochastic calculus of jump-diffusion processes to calculate the rate of stochastic entropy production for instantaneous resetting, and show how previous results are recovered upon averaging over sample trajectories. Second, we formulate single-particle diffusion in a switching potential as a hybrid SDE and develop a hybrid extension of Itô’s stochastic calculus to derive a general expression for the rate of stochastic entropy production. We illustrate the theory by considering overdamped Brownian motion in an intermittent harmonic potential. Finally, we calculate the average rate of entropy production for a population of non-interacting Brownian particles moving in a common switching potential. In particular, we show that the latter induces statistical correlations between the particles, which means that the total entropy is not given by the sum of the 1-particle entropies.

The temporal asymmetry of cortical dynamics as a signature of brain states

The brain is a complex non-equilibrium system capable of expressing many different dynamics as well as the transitions between them. We hypothesized that the level of non-equilibrium can serve as a signature of a given brain state, which was quantified using the arrow of time (the level of irreversibility). Using this thermodynamic framework, the irreversibility of emergent cortical activity was quantified from local field potential recordings in male Lister-hooded rats at different anesthesia levels and during the sleep-wake cycle. This measure was carried out on five distinct brain states: slow-wave sleep, awake, deep anesthesia–slow waves, light anesthesia–slow waves, and microarousals. Low levels of irreversibility were associated with synchronous activity found both in deep anesthesia and slow-wave sleep states, suggesting that slow waves were the state closest to the thermodynamic equilibrium (maximum symmetry), thus requiring minimum energy. Higher levels of irreversibility were found when brain dynamics became more asynchronous, for example, in wakefulness. These changes were also reflected in the hierarchy of cortical dynamics across different cortical areas. The neural dynamics associated with different brain states were characterized by different degrees of irreversibility and hierarchy, also acting as markers of brain state transitions. This could open new routes to monitoring, controlling, and even changing brain states in health and disease.

Predicting Dependent Edges in Nonequilibrium Complex Systems Based on Overlapping Module Characteristics

Problem: Predicting dependency relationships in nonequilibrium systems is a critical challenge in complex systems research. Solution proposed: In this paper, we propose a novel method for predicting dependent edges in network models of nonequilibrium complex systems, based on overlapping module features. This approach addresses the many-to-many dependency prediction problem between nonequilibrium complex networks. By transforming node-based network models into edge-based models, we identify overlapping modular structures, enabling the prediction of many-to-many dependent edges. Experimental evaluation: This method is applied to dependency edge prediction in power and gas networks, curriculum and competency networks, and text and question networks. Results: The results indicate that the proposed dependency edge prediction method enhances the robustness of the network in power–gas networks, accurately identifies supporting relationships in curriculum–competency networks, and achieves better information gain in text–question networks. Conclusion: These findings confirm that the overlapping module-based approach effectively predicts dependencies across various nonequilibrium complex systems in diverse fields.

A local–global principle for nonequilibrium steady states

The global steady state of a system in thermal equilibrium exponentially favors configurations with lesser energy. This principle is a powerful explanation of self-organization because energy is a local property of configurations. For nonequilibrium systems, there is no such property for which an analogous principle holds, hence no common explanation of the diverse forms of self-organization they exhibit. However, a flurry of recent empirical results has shown that a local property of configurations called "rattling" predicts the steady states of some nonequilibrium systems, leading to claims of a far-reaching principle of nonequilibrium self-organization. But for which nonequilibrium systems is rattling accurate, and why? We develop a theory of rattling in terms of Markov processes that gives simple and precise answers to these key questions. Our results show that rattling predicts a broader class of nonequilibrium steady states than has been claimed and for different reasons than have been suggested. Its predictions hold to an extent determined by the relative variance of, and correlation between, the local and global "parts" of a steady state. We show how these quantities characterize the local-global relationships of various random walks on random graphs, spin-glass dynamics, and models of animal collective behavior. Surprisingly, we find that the core idea of rattling is so general as to apply to equilibrium and nonequilibrium systems alike.

Energy Aware Technology Mapping of Genetic Logic Circuits.

Energy and its dissipation are fundamental to all living systems, including cells. Insufficient abundance of energy carriers─as caused by the additional burden of artificial genetic circuits─shifts a cell's priority to survival, also impairing the functionality of the genetic circuit. Moreover, recent works have shown the importance of energy expenditure in information transmission. Despite living organisms being non-equilibrium systems, non-equilibrium models capable of accounting for energy dissipation and non-equilibrium response curves are not yet employed in genetic design automation (GDA) software. To this end, we introduce Energy Aware Technology Mapping, the automated design of genetic logic circuits with respect to energy efficiency and functionality. The basis for this is an energy aware non-equilibrium steady state model of gene expression, capturing characteristics like energy dissipation─which we link to the entropy production rate─and transcriptional bursting, relevant to eukaryotes as well as prokaryotes. Our evaluation shows that a genetic logic circuit's functional performance and energy efficiency are disjoint optimization goals. For our benchmark, energy efficiency improves by 37.2% on average when comparing to functionally optimized variants. We discover a linear increase in energy expenditure and overall protein expression with the circuit size, where Energy Aware Technology Mapping allows for designing genetic logic circuits with the energetic costs of circuits that are one to two gates smaller. Structural variants improve this further, while results show the Pareto dominance among structures of a single Boolean function. By incorporating energy demand into the design, Energy Aware Technology Mapping enables energy efficiency by design. This extends current GDA tools and complements approaches coping with burden in vivo.

Capturing non-Markovian polaron dressing with the master equation formalism.

Understanding the dynamics of open quantum systems in strong coupling and non-Markovian regimes remains a formidable theoretical challenge. One popular and well-established method of approximation in these circumstances is provided by the polaron master equation (PME). In this work, we re-evaluate and extend the validity of the PME to capture the impact of non-Markovian polaron dressing, induced by non-equilibrium open system dynamics. By comparing with numerically exact techniques, we confirm that while the standard PME successfully predicts the dynamics of system observables that commute with the polaron transformation (e.g., populations in the Pauli z-basis), it can struggle to fully capture those that do not (e.g., coherences). This limitation stems from the mixing of system and environment degrees of freedom inherent to the polaron transformation, which affects the accuracy of calculated expectation values within the polaron frame. Employing the Nakajima-Zwanzig projection operator formalism, we introduce correction terms that provide an accurate description of observables that do not commute with the transformation. We demonstrate the significance of the correction terms in two cases, the canonical spin-boson model and a dissipative time-dependent Landau-Zener protocol, where they are shown to impact the system dynamics on both short and long timescales.

Decomposing Thermodynamic Dissipation of Linear Langevin Systems via Oscillatory Modes and Its Application to Neural Dynamics

Recent developments in stochastic thermodynamics have elucidated various relations between the entropy production rate (thermodynamic dissipation) and the physical limits of information processing in nonequilibrium dynamical systems. These findings have been actively utilized and have opened new perspectives in the analysis of real biological systems. In neuroscience also, the importance of quantifying entropy production has attracted increasing attention as a means to understand the properties of information processing in the brain. However, the relationship between entropy production rate and oscillations, which is prevalent in many biological systems, is unclear. For example, neural oscillations, such as delta, theta, and alpha waves, play crucial roles in brain information processing. Here, we derive a novel decomposition of the entropy production rate of linear Langevin systems. We show that one of the components of the entropy production rate, called the housekeeping entropy production rate, can be decomposed into independent positive contributions from oscillatory modes. Our decomposition enables us to calculate the contribution of oscillatory modes to the housekeeping entropy production rate. In addition, when the noise matrix of the Langevin equation is diagonal, the contribution of each oscillatory mode is further decomposed into the contribution of each element of the system. To demonstrate the utility of our decomposition, we apply our decomposition to an electrocorticography dataset recorded during awake and anesthetized conditions in monkeys, wherein the properties of oscillations change drastically. We show the consistent trends across different monkeys; i.e., the contribution of oscillatory modes from the delta band are larger in the anesthetized condition than in the awake condition, while those from the higher-frequency bands, such as the theta band, are smaller. These results allow us to interpret the change in neural oscillation in terms of stochastic thermodynamics and the physical limit of information processing. Published by the American Physical Society 2024

Reduction-Induced Self-Propelled Oscillatory Motion of Perylenediimides on Water.

The emergence of macroscopic self-propelled oscillatory motion based on molecular design has attracted continual attention in relation to autonomous systems in living organisms. Herein, a series of perylenediimides (PDIs) with various imide side chains was prepared to explore the impact of molecular design and alignment on the self-propelled motion at the air-water interface. When placed on an aqueous solution containing a reductant, a solid disk of neutral PDI was reduced to form the water-soluble, surface-active PDI dianion species, which induces a surface tension gradient in the vicinity of the disk for self-propelled motion. We found that centimeter-scale oscillatory motion could be elicited by controlling the supply rate of PDI dianion species through the reductant concentration and the structure of the imide side chains. Furthermore, we found that the onset and speed of the self-propelled motion could be changed by the crystallinity of PDI at the water surface. This design principle using π-conjugated molecules and their self-assemblies could advance self-propelled, non-equilibrium systems powered by chemical energy.

‘IT FROM BIT’: How does information shape the structures in the Universe?

Based on a synthesis of three main ingredients: (i) the Shannon information in non-equilibrium systems, (ii) the semiclassical energy-time quantization rule and (iii) the quasi-static information-energy correspondence, a new general rule for the quantization of quasi-static information states supported by an environment away from equilibrium is introduced if the history of the environment is known as a function of time in terms of its thermodynamic potential for information T ( t ) Δ S ( t ) that is a free energy measuring the distance from equilibrium Δ S ( t ) , and T ( t ) is the mean temperature of the environment at time t . This all new quasi-static information-time quantization rule is applied to the expanding Universe using a phenomenological thermodynamic potential for information in the matter-dominated era in order to find the eigen-information of the persistent structures that are supported by the universe (or the local environments therein) at any given epoch, thus providing an information–theoretic foundation for formation of structures and rise of complexity with time that embodies the cosmic evolution as epitomized by the late Wheeler’s famous conjecture ‘it from bit’. This theoretical procedure must also open new avenues for further research into the quantum theory of information and complexity in non-equilibrium thermodynamics.

Theoretical Description of Pump-Probe Experiments in Charge-Density-Wave Materials out to Long Times

We describe coupled nonequilibrium electron-phonon systems semiclassically—Ehrenfest dynamics for the phonons and quantum mechanics for the electrons—using a classical Monte Carlo approach that determines the nonequilibrium response to a large pump field. The semiclassical approach is expected to be accurate, because the phonons are excited to average energies much higher than the phonon frequency, eliminating the need for a quantum description. The numerical efficiency of this method allows us to perform a self-consistent time evolution out to very long times (tens of picoseconds), enabling us to model pump-probe experiments of a charge-density-wave (CDW) material. Our system is a half-filled, one-dimensional (1D) Holstein chain that exhibits CDW ordering due to a Peierls transition. The chain is subjected to a time-dependent electromagnetic pump field that excites it out of equilibrium, and then a second probe pulse is applied after a time delay. By evolving the system to long times, we capture the complete process of lattice excitation and subsequent relaxation to a new equilibrium, due to an exchange of energy between the electrons and the lattice, leading to lattice relaxation at finite temperatures. We employ an indirect (impulsive) driving mechanism of the lattice by the pump pulse due to the direct driving of the electrons. We identify two driving regimes, where the pump can either cause small perturbations or completely invert the initial CDW order. Our work successfully describes the ringing of the amplitude mode in CDW systems that has long been seen in experiment but never successfully explained by microscopic theory. We also describe the fluence-dependent crossover that inverts the CDW order parameter and changes the phonon dynamics. Finally, we illustrate how this method can examine a number of different types of experiments including photoemission, x-ray diffraction, and two-dimensional (2D) spectroscopy. Published by the American Physical Society 2024

Maximization of entropy production during vibration in a suspension based on graphite and silicone oil.

The electrical conductivity of a suspension of graphite and silicone oil in the presence of a small electric potential difference and vibration (40÷50Hz) is considered. The concentration of the suspension was selected near the percolation threshold. It has been found that such a nonequilibrium system evolves to increase its dissipation power, and low-energy vibrations accelerate, and high-energy ones hinder this process. Since the dissipation power of the considered system is proportional to entropy production, the results obtained are consistent with the so-called maximum entropy production principle (MEPP). This is the first experimental confirmation of MEPP in the case of a nonequilibrium process with continuous transformations under conditions for the emergence of alternative variants for the development. The possibility of choice among alternatives in a complex system is a fundamental point in the experimental discussion of MEPP, and it was previously underestimated.

Energy Aware Technology Mapping of Genetic Logic Circuits.

Energy and its dissipation are fundamental to all living systems, including cells. Insufficient abundance of energy carriers -as caused by the additional burden of artificial genetic circuits- shifts a cell's priority to survival, also impairing the functionality of the genetic circuit. Moreover, recent works have shown the importance of energy expenditure in information transmission. Despite living organisms being non-equilibrium systems, non-equilibrium models capable of accounting for energy dissipation and non-equilibrium response curves are not yet employed in genetic design automation (GDA) software. To this end, we introduce Energy Aware Technology Mapping, the automated design of genetic logic circuits with respect to energy efficiency and functionality. The basis for this is an energy aware non-equilibrium steady state (NESS) model of gene expression, capturing characteristics like energy dissipation -which we link to the entropy production rate- and transcriptional bursting, relevant to eukaryotes as well as prokaryotes. Our evaluation shows that a genetic logic circuit's functional performance and energy efficiency are disjoint optimization goals. For our benchmark, energy efficiency improves by 37.2% on average when comparing to functionally optimized variants. We discover a linear increase in energy expenditure and overall protein expression with the circuit size, where Energy Aware Technology Mapping allows for designing genetic logic circuits with the energy efficiency of circuits that are one to two gates smaller. Structural variants improve this further, while results show the Pareto dominance among structures of a single Boolean function. By incorporating energy demand into the design, Energy Aware Technology Mapping enables energy efficiency by design. This extends current GDA tools and complements approaches coping with burden in vivo.

Comparison of different thermostat settings in the implicit solvent approach for nanoparticles through brush-decorated nanopores.

Nanoparticles (NPs) that are forcefully driven through a brush-decorated nanochannel form a nonequilibrium system with a rich physical behavior, including a dynamical phase transition between two modes of propagation that correspond to either separate clusters of NPs or a continuous flow channel. The peculiar properties of this system make it an ideal benchmark candidate for a comparison of three thermostat settings, the dissipative particle dynamics (DPD), the Langevin (LGV)dynamics, and a modified LGV setup, denoted as LGV^{-}, in which the thermostatting is disabled in the direction of the driving force. We demonstrate that the choice of the thermostat has little influence on the conformations of NPs, and that, due to differences in the dissipation modes, notable differences arise in their dynamical properties, such as effective friction constants and average velocities. This also includes differences in the coupling between NP clusters and the surrounding brush and affects the corresponding phase diagrams of the two propagation modes. We conclude that the conventional DPD and LGV thermostats yield results that display a reasonable degree of coincidence, but we cannot recommend the use of the LGV^{-} algorithm for the present system.