Thermodynamic Fluctuations Research Articles

Kinetics of Nonequilibrium Melting of a Macrosystem Under the Action of a Volume Heat Source

A kinetic model of nonequilibrium melting of a macrosystem under the action of a volume heat source formed in its bulk has been constructed. In this model, the melting of such a system is defined with account of the thermodynamic fluctuations of its order parameter, playing a great role in the superheating of the system and in the attainment by it of the absolute instability point at which the initially metastable solid phase of the system becomes absolutely unstable relative to the infinitely small fluctuations of its liquid phase. Analytical solutions of the kinetic equations defining the melting of a macrosystem have been obtained for different rates of its heating by an internal volume heat source.

Determination of critical superconducting parameters based on the study of the magnetization fluctuations for RE3Ba5Cu8O18-δ (RE= Sm, Eu, Gd, Dy and Ho) ceramic superconductor system

In this paper, we report the production of cuprate-like superconductor RE3Ba5Cu8O18-δ (RE-358, RE = Dy, Gd, Sm, Eu and Ho) by using the solid reaction method. By means of vibrating sample magnetometry technique (VSM), magnetization curves as a function of temperature were acquired in a Zero Field Cooled/Field Cooled (ZFC/FC) mode. Critical temperature Tc and irreversibility temperature Tirr values were obtained from magnetization curves. The irreversibility line was constructed with Tirr data, it showed an Almeida-Thouless dominant trend for low magnetic fields and Gabay-Toulose behavior for high magnetic fields. Thermodynamic fluctuations were analyzed on magnetic measurements using Bulavskii, Ledvij y Kogan model (BKL) that analyze the vortex fluctuations on Lawrence-Doniach (LD) framework. With this model, penetration length parameters λab and ab-plane coherence length ξab band c-direction ξc was obtained. Crossing point coordinates of the excess magnetization vs. temperature curves for different applied magnetic field amplitudes T* and ΔMab* were determined. Weak magnetic fields were fitted at Δχ/T limit as a function of reduced temperature ε (≥10−2). This procedure allowed us to obtain the mid-field transition temperature value Tc0. Likewise, As (Schmidt diamagnetism) and BLD (LD parameter) constants were found for each of the RE-358 system samples. This showed that through thermodynamic fluctuations analysis, RE-358 system has an excellent bidimensional behavior (2D) and it is strongly anisotropic.

Salt-induced LCST-type thermal gelation of methylcellulose: quantifying non-specific interactions via fluctuation theory.

What drives the phase separation of water-soluble polymers in the presence of electrolytes was quantified on a molecular scale via statistical thermodynamic fluctuation theory. Quantifying polymer-water and polymer-salt interactions enabled us to identify the dominant interaction for phase separation. As a model system, the lower critical solution temperature (LCST) type thermal gelation of methylcellulose (MC) in aqueous salt solutions was chosen. The Kirkwood-Buff integrals for intermolecular interactions, calculated from the published calorimetric and volumetric data, showed that (1) the accumulation of salts around MC molecules (favourable interaction between salts and MC) inhibits thermal gelation and the depletion of salts from MC (unfavourable interaction between salts and MC) promotes the gelation, and (2) this salt-MC interaction is the dominant factor (50-100 times stronger than the water-MC interaction). This insight from the fluctuation theory is at odds with the age-old consensus regarding the driving force of thermal gelation: water structure change in the presence of salts induces the promotion or inhibition of thermal gelation. However, our conclusion is founded upon the ability of the fluctuation theory to quantify water-MC and salt-MC interaction independently via the Kirkwood-Buff integrals. Flory-Huggins (FH) theory, on the contrary, could not separate these two interactions owing to the lack of a thermodynamic degree of freedom because the lattice solution is assumed to be fully packed. In addition, the dominant contribution from salt depletion poses difficulty for the χ parameter, which is essentially the difference of contact energies. Our approach, requiring calorimetric and volumetric data alone as input, provides a simple and versatile method towards elucidating the effect of cosolvents on biopolymer phase separation of physiological importance.

Polymer tethered graphene oxide influences miscibility and cooperative relaxation in LCST blends

The miscibility of a classical lower critical solution temperature (LCST) system; PMMA/SAN was probed by different rheological fingerprints such as isochronal temperature ramps, and isothermal frequency sweeps, in presence of graphene oxide (GO) and PMMA tethered GO. The chain length of the grafted polymer was varied to study its effect on miscibility, volume cooperativity, entanglement density and localization in the blends. The PMMA tethered GO alters the chain dynamics both at local and cooperative length scale through entropic and enthalpic interactions. It was perceived that the thermodynamic miscibility, cooperative relaxations and concentration fluctuation in PMMA/SAN blends are controlled by the spatial distribution of GO in the blend. By varying the chain length, we were able to understand that shorter tethered chains lead to early phase separation whereas the tethered chain length similar to that of the host matrix delays phase separation. Interestingly, irrespective of the length of the tethered polymer chain, the grafted GO sheets were not localized in the thermodynamically preferred phase (here PMMA). These findings are of great importance to further help us understand the theories and simulations which pertain to chain dynamics of PMMA/SAN blends containing polymer-tethered nanoparticles with large specific surface area like GO.

Thermodynamic uncertainty relation for underdamped Langevin systems driven by a velocity-dependent force.

Recently, it has been shown that there is a trade-off relation between thermodynamic cost and current fluctuations, referred to as the thermodynamic uncertainty relation (TUR). The TUR has been derived for various processes, such as discrete-time Markov jump processes and overdamped Langevin dynamics. For underdamped dynamics, it has recently been reported that some modification is necessary for application of the TUR. However, the previous TUR for underdamped dynamics is not applicable to a system driven by a velocity-dependent force. In this study, we present a TUR, applicable to a system driven by a velocity-dependent force in the context of underdamped Langevin dynamics, by extending the theory of Vu and Hasegawa [Phys. Rev. E 100, 032130 (2019)2470-004510.1103/PhysRevE.100.032130]. We show that our TUR accurately describes the trade-off properties of a molecular refrigerator (cold damping), Brownian dynamics in a magnetic field, and an active particle system.

Ruppeiner geometry, phase transitions, and the microstructure of charged AdS black holes

Originally considered for van der Waals fluids and charged black holes [Phys. Rev. Lett. 123, 071103 (2019)], we extend and generalize our approach to higher-dimensional charged AdS black holes. Beginning with thermodynamic fluctuations, we construct the line element of the Ruppeiner geometry and obtain a universal formula for the scalar curvature $R$. We first review the thermodynamics of a van der Waals fluid and calculate the coexistence and spinodal curves. From this we are able to clearly display the phase diagram. Notwithstanding the invalidity of the equation of state in the coexistence phase regions, we find that the scalar curvature is always negative for the van der Waals fluid, indicating that attractive interactions dominate amongst the fluid microstructures. Along the coexistence curve, the scalar curvature $R$ decreases with temperature, and goes to negative infinity at a critical temperature. We then numerically study the critical phenomena associated with the scalar curvature. We next consider four-dimensional charged AdS black holes. Vanishing of the heat capacity at constant volume yields a divergent scalar curvature. In order to extract the corresponding information, we define a new scalar curvature that has behaviour similar to that of a van der Waals fluid. We analytically confirm that at the critical point of the small/large black hole phase transition, the scalar curvature has a critical exponent 2, and $R(1-\tilde{T})^{2}C_{v}=1/8$, the same as that of a van der Waals fluid. However we also find that the scalar curvature can be positive for the small charged AdS black hole, implying that repulsive interactions dominate among the black hole microstructures. We then generalize our study to higher-dimensional charged AdS black holes.

Detonation initiation by compressible turbulence thermodynamic fluctuations

Theory and computations have established that thermodynamic gradients created by hot spots in reactive gas mixtures can lead to spontaneous detonation initiation. However, the current laminar theory of the temperature-gradient mechanism for detonation initiation is restricted to idealized physical configurations. Thus, it only predicts conditions for the onset of detonations in quiescent gases, where an isolated hot spot is formed on a timescale shorter than the chemical and acoustic timescales of the gas. In this work, we extend the laminar temperature-gradient mechanism into a statistical model for predicting the detonability of an autoignitive gas experiencing compressible isotropic turbulence fluctuations. Compressible turbulence forms non-monotonic temperature fields with tightly-spaced local minima and maxima that evolve over a range of timescales, including those much larger than chemical and acoustic timescales. We examine the utility of the adapted statistical model through direct numerical simulations of compressible isotropic turbulence in premixed hydrogen-air reactants for a range of conditions. We find strong, but not conclusive, evidence that the model can predict the degree of detonability in an autoignitive gas due to turbulence-induced thermodynamic gradients.

Resolvent-based study of compressibility effects on supersonic turbulent boundary layers

The resolvent formulation of McKeon & Sharma (2010) is applied to supersonic turbulent boundary layers to study the validity of Morkovin's hypothesis, which postulates that high-speed turbulence structures in zero pressure-gradient turbulent boundary layers remain largely the same as its incompressible counterpart. Supersonic zero-pressure-gradient turbulent boundary layers with adiabatic wall boundary conditions at Mach numbers ranging from 2 to 4 are considered. Resolvent analysis highlights two distinct regions of the supersonic turbulent boundary layer in the wave parameter space: the relatively supersonic region and the relatively subsonic region. In the relatively supersonic region, where the flow is supersonic relative to the freestream, resolvent modes display structures consistent with Mach wave radiation that are absent in the incompressible regime. In the relatively subsonic region, we show that the low-rank approximation of the resolvent operator is an effective approximation of the full system and that the response modes predicted by the model exhibit universal and geometrically self-similar behaviour via a transformation given by the semi-local scaling. Moreover, with the semi-local scaling, we show that the resolvent modes follow the same scaling law as their incompressible counterparts in this region, which has implications for modelling and the prediction of turbulent high-speed wall-bounded flows. We also show that the thermodynamic variables exhibit similar mode shapes to the streamwise velocity modes, supporting the strong Reynolds analogy. Finally, we demonstrate that the principal resolvent modes can be used to capture the energy distribution between momentum and thermodynamic fluctuations.

Thermal phase fluctuations in optically pumped dual-frequency vertical external-cavity surface-emitting lasers for cesium clocks based on coherent population trapping

A fully analytical model is established for the thermal fluctuations of the beatnote phase of an optically pumped dual-frequency vertical-external-cavity surface-emitting laser (VECSEL). This model starts with the resolution of the heat equation inside the semiconductor chip structure and follows with the evaluation of the induced thermo-optic phase shift. Both the fluctuations of the heat induced by the optical pumping and the thermodynamic fluctuations at room temperature are considered. On the one hand, the thermal response of the structure is investigated and a significant thermal lens effect caused by the pump is deduced. On the other hand, the power spectral density of the frequency noise is calculated in the presence of diffusion spatial anisotropy. The present model is in very good agreement with the phase noise measured for a dual-frequency VECSEL at 852 nm for application to metrology and the validity of the usual low-pass filter model is discussed.

Effect of turbulent Mach number on the thermodynamic fluctuations in canonical shock-turbulence interaction

Shock waves can generate high levels of turbulent fluctuations in temperature, pressure and other thermodynamic properties. These have significant role in turbulent mixing, heat transfer and acoustic noise in high-speed flows. The thermodynamic fluctuations generated by canonical shock-turbulence interaction are strong functions of the shock strength and the upstream turbulence intensity. For a fixed shock Mach number, the downstream thermodynamic variances, normalized by the upstream turbulence kinetic energy, are found to increase with the incoming turbulent Mach number (Mt). This is in contrast to the trend observed for Reynolds stresses and the turbulent dissipation rate. We use direct numerical simulations and linear interaction analysis to investigate the effect of Mt on the post-shock thermodynamic field. It is found that the presence of small amount of acoustic and entropy fluctuations in the incoming flow can explain the high intensity of the post shock thermodynamic variances in the high Mt cases.

Self-assembly of active core corona particles into highly ordered and self-healing structures.

Formation of highly ordered structures usually needs to overcome a high free-energy barrier that is greatly beyond the ability of thermodynamic fluctuation such that the system would be easily trapped into a state with many defects and the annealing process of which often occurs on unreachable long time scales. Here, we report theoretically a fascinating example that active core corona particles can successfully self-assemble into a large-scaled and highly ordered stripe or trimer lattice, which is hardly achieved in a nondriven equilibrium system. Besides, such an activity-induced ordered structure shows an interesting self-healing feature of defects. In addition, there exists an optimal level of activity that most favorably enhances the formation of ordered self-assembly structures. Since core corona particles act as important units for self-assembly in real practice, we believe that our study opens a new design-strategy for highly ordered materials.

Supercritical behavior of thermodynamic systems

It is known that basic stability characteristics of a system are inversely proportional to fluctuations of external parameters. Above the critical point there is a region remaining homogeneous macroscopically, but becoming microheterogeneous within an interval of thermodynamic forces. Within this interval thermodynamic coefficients of stability pass finite non-zero minima. This corresponds to the considerable growth of fluctuations and indicates the occurrence of supercritical transition of continuous kind. The limit case of such continuous phase transitions is the critical state, which is also the limit point of some first-kind transitions (the limit point of phase equilibrium curve).In this paper we consider the relation between thermodynamic stability conditions and fluctuations of external parameters of the system. We study the behavior of a simple one-component thermodynamic system (liquid, magnet, and ferroelectric) in the supercritical region and derive the equation of the line of supercritical transition for this system.

The structure and property characteristics of Mn-doped SiGe alloy nanowires prepared by catalyst-free growth

Mn-doped SiGe nanowires (Mn-SGNWs) have been grown on silicon substrates by using simple thermal evaporation without catalyst. TEM and EDS studies indicate the SGNWs are amorphous and the approximate atomic ratio of Si:Ge:Mn is 93.5: 3.6:2.9. Detailed Raman and XRD studies reveal the short-range ordered structure and phase components in the SGNWs, which results in the enhanced magnetization of one order of magnitude higher than that of amorphous Si93.5Mn3.7:H thin films at room temperature. Optical studies show that the samples possess an optical band gap of ∼3.9 eV, exhibit a sharp absorption at 319 nm and emit intense violet and blue light under 325-nm photon excitation with small thermal quenching, which extends the potential application of amorphous SiGe materials into shorter-wavelength UV and visible region. Finally, the catalyst-free growth mechanism for the Mn-SGNWs is proposed by considering phase diagram and the critical role of thermodynamic fluctuation during the growth. Our results may be valuable for both basic science and potential applications of SGNW based materials.

Repulsive Interactions and Universal Properties of Charged Anti–de Sitter Black Hole Microstructures

The Ruppeiner geometry of thermodynamic fluctuations provides a powerful diagnostic of black hole microstructures. We investigate this for charged anti-de Sitter black holes and find that, while an attractive microstructure interaction dominates for most parameter ranges, a weak repulsive interaction dominates for small black holes of high temperature. This unique property distinguishes the black hole system from that of a van der Waals fluid, where only attractive microstructure interactions are found. We also find two other novel universal properties for charged black holes. One is that the repulsive interaction is independent of the black hole charge and temperature. The other is that the behavior of the Ruppeiner curvature scalar near criticality is characterized by a dimensionless constant that is identical to that for a van der Waals fluid, providing us with new insight into black hole microstructures.

Convergence of thermodynamic quantities and work fluctuation theorems in the presence of random protocols

Recently, many results, namely the Fluctuation theorems (FT), have been discovered for systems arbitrarily away from equilibrium. Many of these relations have been experimentally tested. The system under consideration is usually driven out of equilibrium by an external time-dependent parameter which follows a particular protocol. One needs to perform several iterations of the same experiment in order to find statistically relevant results. Since the systems are microscopic, fluctuations dominate. Studying the convergence of relevant thermodynamics quantities with number of realizations is also important as it gives a rough estimate of the number of iterations one needs to perform. In each iteration, the protocol follows a predetermined identical/fixed form. However, the protocol itself may be prone to fluctuations. In this work, we are interested in looking at a simple nonequilibrium system, namely a Brownian particle trapped in a harmonic potential. The center of the trap is then dragged according to a protocol. We however lift the condition of fixed protocol. In our case, the protocol in each realization is different. We consider one of the parameters of the protocol as a random variable, chosen from some known distribution. We study the systems analytically as well as numerically. We specifically study the convergence of the average work and free energy difference with number of realizations. Interestingly, in several cases, randomness in the protocol does not seem to affect the convergence when compared to fixed protocol results. We study symmetry functions. The cases of a Brownian particle in a harmonic potential with sinusoidally changing stiffness constant, as well as a Brownian particle in a double well potential, are also studied. We believe that our results can be experimentally verified.

Density Functional Study on Enhancement of Modulus of Confined Fluid in Nanopores

Elastic modulus in fluid is a crucial thermodynamic property due to its close relation to the viscoelastic behaviors in dynamics and the pore size analysis in porous materials. Especially, elasticity in nanoconfined fluid, which exhibits significant deviation from that of bulk fluid, has gained a multitude of applications in industrial and engineering fields. In this work, general expressions of bulk and shear moduli for inhomogeneous fluids have been derived based on Hooke’s law. In the bulk phase, the obtained moduli reduce exactly to those obtained from thermodynamic fluctuation theory. In addition, both moduli have been expressed as functionals of fluid density functions. Besides, the Cauchy relation and Voigt notation for inhomogeneous elasticity have been first obtained. The validity of the obtained moduli has been verified through their comparison with grand canonical Monte Carlo simulation. Our further calculations suggest that the bulk modulus of confined fluid is inhomogeneous across the pore an...

Phase Transitions in Helicoidal Ferromagnets with Concentrational Fluctuations of Local Magnetization

A phenomenological approach to the theory of phase transitions induced by fluctuations in helicoidal ferromagnets with concentrational fluctuations is developed. For this purpose, random variables equal to one at a site ν occupied by a magnetic atom and zero otherwise are introduced into the Ginzburg–Landau functional. It is shown that, above the magnetic transition temperature (TC), due to concentrational effects, local magnetization is preserved, fluctuations of the helicoidal spin helix arise, and skyrmion states in the magnetic field are formed. The disappearance of the vortical states is due to the suppression of local magnetization by thermodynamic fluctuations at the temperature TS (>TC). The theoretical results explain the reasons for the significant expansion of the temperature range of skyrmion states in nonstoichiometric manganese monosilicide with manganese deficiency.

Electronic structure and phase transitions in MnSi

• Within the framework of the spin-fluctuation theory, a strongly correlated MnSi is investigated taking into account the LDA spectrum and the Dzyaloshinsky –Moria interaction. • The phase transition in an external magnetic field is accompanied by a sharp suppression of zero spin fluctuations and the appearance of the skyrmion phase. • As a result of the disappearance of zero spin fluctuations, the chemical potential is in the region of the local minimum and chiral ferromagnetism becomes thermodynamically unstable. • The temperature increase of thermodynamic fluctuations leads to a first-order phase transition from the skyrmion phase to the paramagnetic phase. • The result of susceptibility calculation is consistent with the experiment.

Asymmetric time-cross-correlation of nonequilibrium concentration fluctuations in a ternary liquid mixture.

Equilibrium phenomena are characterized by time symmetry. Thermodynamic fluctuations are also time-symmetric at equilibrium. Conversely, diffusion of a solute in a liquid in the presence of a gradient is a nonequilibrium phenomenon, which gives rise to long-range fluctuations with amplitude much larger than the equilibrium one for small enough wave number. In the case of diffusion in binary mixtures such fluctuations are time-symmetric, notwithstanding the fact that they are generated by a nonequilibrium condition. In this paper, we investigate diffusion of two solutes in a ternary liquid mixture by means of fluctuating hydrodynamics theory. We show that the time-cross-correlation function of the concentrations is not time-symmetric, hence showing that time symmetry is violated for such nonequilibrium fluctuations. We discuss the feasibility of experiments aimed at the detection of the asymmetry of the cross-correlation function of nonequilibrium concentration fluctuations in ternary mixtures, as envisaged in the Giant Fluctuations (NEUF-DIX) microgravity project of the European Space Agency.

Global Quantum Discord in Transverse‐Field Ising Models on N × N Square Lattices

Global quantum discord (GQD) in two‐dimensional (2D) transverse‐field Ising models on N × N square lattices at zero temperature and finite temperatures are studied. First, the GQD defined on the reduced density matrix of a 2 × 2 sub‐square in the center of the N × N lattices, with is studied. It is found that shows little size dependence in the strong‐field and weak‐field limit, and presents dramatic size dependence in the middle‐field region. The results are explained by short‐range correlations in non‐critical regions and long‐range correlations in critical regions of the models, respectively. Then the scaling behavior of the GQD of the ground states for the entire N × N squares is studied. It is found that contains a 1D contribution (corresponding to the side length of the squares) and a 2D contribution (corresponding to the area of the squares). Furthermore, the effect of thermodynamic fluctuations on GQD by investigating the thermal‐state GQD is considered. In high‐temperature regions, GQD is always destroyed by thermodynamic fluctuations for any strength of the magnetic field. However, in low‐temperature regions, some thermal enhancement of GQD under weak fields and some thermal robustness of GQD under strong fields is observed. The results are explained by the low‐lying energy states and the energy gap of the models.