Thermodynamic Limit Research Articles

Self-propelled collective motion with multiplicative scalar noise

The emergence of order from initial disordered movement in self-propelled collective motion is an instance of nonequilibrium phase transition, which is known to be first order in the thermodynamic limit. Here, we introduce a multiplicative scalar noise model of collective motion as a modification of the original Vicsek model, which more closely mimics the particles’ behavior. We allow for more individual movement in sparsely populated neighborhoods, the mechanism of which is not incorporated in the original Vicsek model. This is especially important in the low velocity and density regime where the probability of a clear neighborhood is relatively high. The modification, thus, removes the shortcoming of the Vicsek model in predicting continuous phase transition in this regime. The onset of collective motion in the proposed model is numerically studied in detail, indicating a first-order phase transition in both high and low velocity/density regimes for systems with comparatively smaller size which is computationally desirable.

Membrane Catalyzed Formation of Nucleotide Clusters and Their Role in the Origins of Life: Insights from Molecular Simulations and Lattice Modeling.

One of the mysteries in studying the molecular "Origin of Life" is the emergence of RNA and RNA-based life forms, where nonenzymatic polymerization of nucleotides is a crucial hypothesis in formation of large RNA chains. The nonenzymatic polymerization can be mediated by various environmental settings, such as cycles of hydration and dehydration, temperature variations, and proximity to a variety of organizing matrices, such as clay, salt, fatty acids, lipid membrane, and mineral surface. In this work, we explore the influence of different phases of the lipid membrane toward nucleotide organization and polymerization in a simulated prebiotic setting. Our molecular simulations quantify the localization propensity of a mononucleotide, uridine monophosphate (UMP), in distinct membrane settings. We perform all-atom molecular dynamics (MD) simulations to estimate the role of the monophasic and biphasic membranes in modifying the behavior of UMPs localization and their clustering mechanism. Based on the interaction energy of mononucleotides with the membrane and their diffusion profile from our MD calculations, we developed a lattice-based model to explore the thermodynamic limits of the observations made from the MD simulations. The mathematical model substantiates our hypothesis that the lipid layers can act as unique substrates for "catalyzing" polymerization of mononucleotides due to the inherent spatiotemporal heterogeneity and phase change behavior.

Validity of annealed approximation in a high-dimensional system

This study investigates the suitability of the annealed approximation in high-dimensional systems characterized by dense networks with quenched link disorder, employing models of coupled oscillators. We demonstrate that dynamic equations governing dense-network systems converge to those of the complete-graph version in the thermodynamic limit, where link disorder fluctuations vanish entirely. Consequently, the annealed-network systems, where fluctuations are attenuated, also exhibit the same dynamic behavior in the thermodynamic limit. However, a significant discrepancy arises in the incoherent (disordered) phase wherein the finite-size behavior becomes critical in determining the steady-state pattern. To explicitly elucidate this discrepancy, we focus on identical oscillators subject to competitive attractive and repulsive couplings. In the incoherent phase of dense networks, we observe the manifestation of random irregular states. In contrast, the annealed approximation yields a symmetric (regular) incoherent state where two oppositely coherent clusters of oscillators coexist, accompanied by the vanishing order parameter. Our findings imply that the annealed approximation should be employed with caution even in dense-network systems, particularly in the disordered phase.

Absence of localization in weakly interacting Floquet circuits

We present a family of Floquet circuits that can interpolate between noninteracting qubits, free propagation, generic interacting, and dual-unitary dynamics. We identify the operator entanglement entropy of the two-qubit gate as a good quantitative measure of the interaction strength. We test the persistence of localization in the vicinity of the noninteracting point by probing spectral statistics, decay of autocorrelators, and measuring entanglement growth. The finite-size analysis suggests that the many-body localized regime does not persist in the thermodynamic limit. Instead, our results are compatible with an integrability-breaking phenomenon. Published by the American Physical Society 2024

Clifford-Deformed Surface Codes

Various realizations of Kitaev’s surface code perform surprisingly well for biased Pauli noise. Attracted by these potential gains, we study the performance of Clifford-deformed surface codes (CDSCs) obtained from the surface code by the application of single-qubit Clifford operators. We first analyze CDSCs on the 3×3 square lattice and find that, depending on the noise bias, their logical error rates can differ by orders of magnitude. To explain the observed behavior, we introduce the effective distance d′, which reduces to the standard distance for unbiased noise. To study CDSC performance in the thermodynamic limit, we focus on random CDSCs. Using the statistical mechanical mapping for quantum codes, we uncover a phase diagram that describes random CDSC families with 50% threshold at infinite bias. In the high-threshold region, we further demonstrate that typical code realizations outperform the thresholds and subthreshold logical error rates, at finite bias, of the best-known translationally invariant codes. We demonstrate the practical relevance of these random CDSC families by constructing a translation-invariant CDSC belonging to a high-performance random CDSC family. We also show that our translation-invariant CDSC outperforms well-known translation-invariant CDSCs, such as the XZZX and XY codes. Published by the American Physical Society 2024

Force-induced desorption of copolymeric comb polymers

We investigate a lattice model of comb copolymers that can adsorb at a surface and that are subject to a force causing desorption. The teeth (the comb’s side chains) and the backbone of the comb are chemically distinct and can interact differently with the surface. That is, the strength of the surface interaction can be different for the monomers in the teeth and in the backbone. We consider several cases including (i) the uniform case where the number of teeth is fixed and the lengths of the branches in the backbone and the lengths of the teeth are all identical, (ii) the case where the teeth are short compared to the branches in the backbone, (iii) the situation where the teeth are long compared to the backbone, and (iv) the case where the number of teeth approaches infinity. We obtain expressions for the free energies in the thermodynamic limit in terms of those for self-avoiding walks and discuss the nature of the phase diagrams of the model.

Exact steady states of the impurity-doped XXZ spin chain coupled to dissipators

We give an exact matrix product steady state and matrix product forms of local observables for the bulk impurity-doped XXZ spin model coupled to dissipators at both ends, whose dynamics is described by the Lindblad quantum master equation. We find that local magnetization is induced at the impurity site when the spin current flows, which is contrary to the usual situation where the current suppresses magnetization due to heating. It is proved that this current-induced magnetization survives in the thermodynamic limit, and the spin current does not depend on the impurity strength. We discuss the role of bulk integrability by comparing the results with those of non-integrable models solved numerically by the quantum trajectory method.

Rotating clusters in phase-lagged Kuramoto oscillators with higher-order interactions.

The effect of phase-lag in pairwise interactions has been a topic of great interest for a while. However, real-world systems often have interactions that are beyond pairwise and can be modeled using simplicial complexes. We show that the inclusion of higher-order interactions in phase-lagged coupled Kuramoto oscillators shifts the critical point at which first-order transition from a cluster synchronized state to an incoherent state takes place. Considering the polar coordinates, we obtain the rotation frequency of the clusters, which turns out to be a function of the phase-lag parameter. In turn, the phase- lag can be used as a control parameter to achieve a desired cluster frequency. Moreover, in the thermodynamic limit, by employing the Ott-Antonsen approach we derive a reduced equation for the order parameter measuring cluster synchronization and progress further through the self-consistency method to obtain a closed form of the order parameter measuring global synchronization which was lacking in the Ott-Antonsen approach.

Enhanced Twist-Averaging Technique for Magnetic Metals: Applications Using Quantum Monte Carlo.

We propose an improved twist-averaging (TA) scheme for quantum Monte Carlo methods that use converged Kohn-Sham or Hartree-Fock orbitals as the reference. This TA technique is tailored to sample the Brillouin zone of magnetic metals, although it naturally extends to nonmagnetic (NM) conducting systems. The proposed scheme aims to reproduce the reference magnetization and achieves charge neutrality by construction, thus avoiding the large energy fluctuations and the postprocessing needed to correct the energies. It shows the most robust convergence of total energy and magnetism to the thermodynamic limit (TDL) when compared to four other TA schemes. Diffusion Monte Carlo applications are shown on NM Al and ferromagnetic α-Fe. The cohesive energy of Al in the TDL shows an excellent agreement with the experimental result. Furthermore, the magnetic moments in α-Fe exhibit rapid convergence with an increasing number of twists.

Many-body quantum chaos in mixtures of multiple species.

We study spectral correlations in many-body quantum mixtures of fermions, bosons, and qubits with periodically kicked spreading and mixing of species. We take two types of mixing, namely, Jaynes-Cummings and Rabi, respectively, satisfying and breaking the conservation of a total number of species. We analytically derive the generating Hamiltonians whose spectral properties determine the spectral form factor in the leading order. We further analyze the system-size (L) scaling of Thouless time t^{*}, beyond which the spectral form factor follows the prediction of random matrix theory. The L dependence of t^{*} crosses over from lnL to L^{2} with an increasing Jaynes-Cummings mixing between qubits and fermions or bosons in a finite-size chain, and it finally settles to t^{*}∝O(L^{2}) in the thermodynamic limit for any mixing strength. The Rabi mixing between qubits and fermions leads to t^{*}∝O(lnL), previously predicted for single species of qubits or fermions without total-number conservation.

Investigating maximum temperature lift potential of the adsorption heat transformer cycle using IUPAC classified isotherms

Adsorption heat transformer (AHT) cycle is capable of upgrading the low-grade waste heat to a higher temperature. The maximum temperature lift of the AHT cycle can represent its theoretical performance limit. However, such a metric is currently absent from the literature due to the scarcity of fundamental studies on the heat upgrading sorption cycles. Therefore, in the present study, three models are proposed to derive the ‘maximum temperature lift’ of a typical AHT cycle: (i) heat engine heat pump representation, (ii) the 2nd law of thermodynamic formulation, and (iii) complete preheating. The first two models are developed based on the reversible cycle approach, whereas the 3rd model incorporates adsorbed phase properties. Thus, the first two models might be considered as the formulations for the thermodynamic temperature limit (lift) of an AHT cycle while the 3rd model is specific to the nature of a particular adsorbent + adsorbate pair which might be close to practical applications. The reversible models predict a maximum temperature lift of 22∘C to 58∘C for heat source temperatures between 50∘C to 80∘C. The 3rd model exhibits lower values of maximum temperature lift compared to the reversible models, owing to the inclusion of material properties in its formulation. The performance of the models is demonstrated by determining the maximum temperature lift of four water-based adsorption working pairs, each featuring distinct IUPAC (International Union of Pure and Applied Chemistry) isotherm types. This study will help propel the working pair selection and the thermodynamic modeling of sorption cycles to achieve its near maximum capability.

Quantum droplets with particle imbalance in one-dimensional optical lattices

We study the formation of particle-imbalanced quantum droplets in a one-dimensional optical lattice containing a binary bosonic mixture at zero temperature. To understand the effects of the imbalance from both the few- and many-body perspectives, we employ density matrix renormalization group (DMRG) simulations and perform the extrapolation to the thermodynamic limit. In contrast to the particle-balanced case, not all bosons are paired, resulting in an interplay between bound states and individual atoms that leads to intriguing phenomena. Quantum droplets manage to sustain a small particle imbalance, resulting in an effective magnetization. However, as the imbalance is further increased, a critical point is eventually crossed, and the droplets start to expel the excess particles while the magnetization in the bulk remains constant. Remarkably, the unpaired particles on top of the quantum droplet effectively form a super Tonks-Girardeau (hard-rod) gas. The expulsion point coincides with the critical density at which the size of the super Tonks-Girardeau gas matches the size of the droplet.

Thermal transitions in a one-dimensional, finite-size Ising model

We revisit the one-dimensional ferromagnetic Ising spin chain with a finite number of spins and periodic boundaries, deriving analytically and verifying numerically its various stationary and dynamical properties at different temperatures. In particular, we determine the probability distributions of magnetization, the number of domain walls, and the corresponding residence times for different chain lengths and magnetic fields. While we study finite systems at thermal equilibrium, we identify several temperatures similar to the critical temperatures for first-order phase transitions in the thermodynamic limit. We illustrate the utility of our results by their application to structural transitions in biopolymers having non-trivial intermediate equilibrium states.

Synchronization transitions in coupled q-deformed logistic maps

The concept of q-deformation has been expanded in a variety of situations including q-deformed nonlinear maps. Coupled q-deformed logistic maps with positive and negative q-diffusive coupling are investigated. The transition to state of synchronized fixed point in the thermodynamic limit for random initial conditions is studied as dynamic phase transitions. Though rare for one-dimensional maps, q-deformed maps show multistability. For weak coupling, the synchronized state may not be observed in the thermodynamic limit with random initial conditions even if it is linearly stable. Thus multistability persists. However, for large lattices with random initial conditions, five well-defined critical points are observed where the transition to a synchronized state occurs. Two of these show continuous phase transition. One of them is in the directed percolation universality class. In another case, the order parameter shows power-law decay superposed with oscillations on a logarithmic scale at the critical point and does not match with known universality classes.

Advancements of MOFs in the Field of Propane Oxidative Dehydrogenation for Propylene Production.

Compared to the currently widely used propane dehydrogenation process for propylene production, propane oxidative dehydrogenation (ODHP) offers the advantage of no thermodynamic limitations and lower energy consumption. However, a major challenge in ODHP is the occurrence of undesired over-oxidation reactions of propylene, which reduce selectivity and hinder industrialization. MOFs possess a large number of metal sites that can serve as catalytic centers, which facilitates the easier access of reactants to the catalytic centers for reaction. Additionally, their flexible framework structure allows for easier adjustment of their pores compared to metal oxides and molecular sieves, which is advantageous for the diffusion of products within the framework. This property reduces the likelihood of prolonged contact between the generated propylene and the catalytic centers, thus minimizing the possibility of over-oxidation. The research on MOF catalyzed oxidative dehydrogenation of propane (ODHP) mainly focuses on the catalytic properties of MOFs with cobalt oxygen sites and boron oxygen sites. The advantages of cobalt oxygen site MOFs include significantly reduced energy consumption, enabling catalytic reactions at temperatures of 230 °C and below, while boron oxygen site MOFs exhibit high conversion rates and selectivity, albeit requiring higher temperatures. The explicit structure of MOFs facilitates the mechanistic study of these sites, enabling further optimization of catalysts. This paper provides an overview of the recent progress in utilizing MOFs as catalysts for ODHP and explores how they promote progress in ODHP catalysis. Finally, the challenges and future prospects of MOFs in the field of ODHP reactions are discussed.

A Perspective on Solar-Driven Electrochemical Routes for Sustainable Methanol Production

The transition towards sustainable and renewable energy sources is imperative in mitigating the environmental impacts of escalating global energy consumption. Methanol, with its versatile applications and potential as a clean energy carrier, a precursor chemical, and a valuable commodity, emerges as a promising solution within the realm of renewable energy technologies. This work explores the integration of electrochemistry with solar power to drive efficient methanol production processes, focusing on electrochemical reduction (ECR) of CO2 and methane oxidation reaction (MOR) as pathways for methanol synthesis. Through detailed analysis and calculations, we evaluate the thermodynamic limits and realistic solar-to-fuel (STF) efficiencies of ECR and MOR. Our investigation encompasses the characterization of multijunction light absorbers, determination of thermoneutral potentials, and assessment of STF efficiencies under varying conditions. We identify the challenges and opportunities inherent in both ECR and MOR pathways, shedding light on catalyst stability, reaction kinetics, and system optimization, thereby providing insights into the prospects and challenges of solar-driven methanol synthesis, offering a pathway towards a cleaner and more sustainable energy future.

Walking with the Atoms in a Chemical Bond: A Perspective Using Quantum Phase Transition.

Phase transitions happen at critical values of the controlling parameters, such as the critical temperature in classical phase transitions, and system critical parameters in the quantum case. However, true criticality happens only at the thermodynamic limit, when the number of particles goes to infinity with constant density. To perform the calculations for the critical parameters, a finite-size scaling approach was developed to extrapolate information from a finite system to the thermodynamic limit. With the advancement in the experimental and theoretical work in the field of ultra-cold systems, particularly trapping and controlling single atomic and molecular systems, one can ask: do finite systems exhibit quantum phase transition? To address this question, finite-size scaling for finite systems was developed to calculate the quantum critical parameters. The recent observation of a quantum phase transition in a single trapped 171 Yb+ ion indicates the possibility of quantum phase transitions in finite systems. This perspective focuses on examining chemical processes at ultra-cold temperatures, as quantum phase transitions-particularly the formation and dissociation of chemical bonds-are the basic processes for understanding the whole of chemistry.

Renormalization of net steered coherence and average coherence in the XXZ model with Dzyaloshinskii–Moriya interaction

The critical behaviors of the net steered coherence (NSC) and average coherence (AC) in the XXZ model with Dzyaloshinskii–Moriya interaction are investigated by adopting the quantum renormalization group method. It is found that they both develop different saturated values in different phases of the model after enough iterations of the renormalization of the coupling constants. In addition, their susceptibilities at the phase transition point are divergent in the thermodynamic limit, and the scaling exponent is determined by the exponent governing the divergence of the correlation length close to the phase transition point. This exemplifies that both the NSC and AC can serve as reliable indicators of quantum phase transitions.

An active and stable catalyst of Zn modified Pt nanoparticles encapsulated within silicalite-1 zeolite for dehydrogenation of ethane

The rapid deactivation of catalysts for ethane dehydrogenation (EDH) at considerably higher temperature and the relatively inert feature of ethane makes it urgent to develop highly active and stable catalysts. Herein, a Zn modified Pt nanoparticles confined within silicalite-1 (S-1) zeolite catalyst for EDH reaction was synthesized by hydrothermal synthesis using the PtZn/SiO2 precursor without any protective ligands, which achieved extremely high catalytic performance (e.g., 15.9 % conversion which was close to the thermodynamic equilibrium limitation, 99.5 % ethylene selectivity, and 0.001 h−1 the deactivation rate). Multiple characterizations with XPS, in situ CO-DRIFTS, in situ C2H6-DRIFTS, TG-DTA, and Raman techniques on these catalysts revealed that the electron-rich Pt sites with stable electronic environment formed by Zn promoter introduced, resulting in enhanced anti-reduction and coke-resistance abilities. Furthermore, characterizations with XRD, HRTEM, Py-IR, hydroxyl vibration region of DRIFT spectra and 1H MAS NMR spectroscopic analysis showed that the dilution effect of Zn and the trapping of zinc and platinum species by Si-OH groups in the form of (≡Si-O-Zn)xPt complex could inhibit migration and aggregation, resulting in smaller metal particles and increase anti-sintering ability. The superior catalytic performance as well as the environmental benign preparation route with no-ligand will further contribute to the advantages for future applications.

Kinetic and Thermodynamic Transition Pathways of Silica by Machine Learning: Implication for Meteorite Impacts

AbstractRocks falling to Earth from space may generate pressure and temperature approaching Earth's deep mantle, but such meteorite impact only persists for a very short period. Under these extreme conditions, kinetical factors largely control mineral phase transitions, in which the resultant phase may deviate from those at thermal equilibrium. Here, we focus on the phase transitions of silica during meteorite impact, and have elucidated multiple pathways from low‐coordinated silica to seifertite, the densest known silica found in meteorite samples. Utilizing a high‐dimensional neuro‐network potential specifically designed for silica, we exhaustively map the potential energy landscape through stochastic surface walking and uncover low‐barrier transition pathways toward seifertite at pressures far away from thermal equilibrium. These kinetic‐driven transitions are then characterized by first‐principles simulations, revealing narrow transition windows of pressure, with seifertite becoming more kinetically favored over stishovite at pressures in the vicinity of 10 and 25 GPa. Our results suggest that meteorite impacts should have reached such target pressures to overcome the thermodynamic limit of forming seifertite. The presence of seifertite may provide key information in constraining the relevant dynamic compression conditions.