Entropy Discontinuities Research Articles

Boundary-induced singularity in strongly-correlated quantum systems at finite temperature

Exploring the bulk-boundary correspondences and the boundary-induced phenomena in the strongly-correlated quantum systems belongs to the most fundamental topics of condensed matter physics. In this work, we study the bulk-boundary competition in a simulative Hamiltonian, with which the thermodynamic properties of the infinite-size translationally-invariant system can be optimally mimicked. The simulative Hamiltonian is constructed by introducing local interactions on the boundaries, coined as the entanglement-bath Hamiltonian (EBH) that is analogous to the heat bath. The terms within the EBH are variationally determined by a thermal tensor network method, with coefficients varying with the temperature of the infinite-size system. By treating the temperature as an adjustable hyper-parameter of the EBH, we identify a discontinuity point of the coefficients, dubbed as the ‘boundary quench point’ (BQP), whose physical implication is to distinguish the point, below which the thermal fluctuations from the boundaries to the bulk become insignificant. Fruitful phenomena are revealed when considering the simulative Hamiltonian, with the EBH featuring its own hyper-parameter, under the canonical ensembles at different temperatures. Specifically, a discontinuity in bulk entropy at the BQP is observed. The exotic entropic distribution, the relations between the symmetries of Hamiltonian and BQP, and the impacts from the entanglement-bath dimension are also explored. Our results show that such a singularity differs from those in the conventional thermodynamic phase transition points that normally fall into the Landau–Ginzburg paradigm. Our work provides the opportunities on exploring the exotic phenomena induced by the competition between the bulk and boundaries.

Vibrational dynamics in the undercooled liquid of ultra-fragile metallic glasses

The lattice vibrational dynamics in ultra-fragile Pt57Cu23P20 and Pt60Cu20P20 glasses were investigated using in situ inelastic neutron scattering to measure the evolution of the phonon density of states (DOS) through the glass transition, into the undercooled liquid phase, and through crystallization. The phonon DOS curves are remarkably similar for the undercooled liquids and the amorphous solids. The vibrational entropy was obtained with these phonon DOS curves, and changes in vibrational entropy caused by the glass transition are less than 0.05kB/atom. For these highly fragile metal/metalloid glasses, the excess vibrational entropy of the undercooled liquid is about 0.5–1.5 J mol−1 K−1, compared to 0.1 J mol−1 K−1 reported earlier for stronger Cu–Zr glasses. Our work suggests that, consistent with our previous report for less fragile metallic glasses, the fraction of the total excess entropy that is vibrational is small, and the discontinuity in excess entropy at the glass transition is mainly due to configurational entropy.

Advection by Large-scale Spiral Flows in Galaxy Clusters

Abstract The intracluster medium of a galaxy cluster often shows an extended quasi-spiral structure, accentuated by tangential discontinuities known as cold fronts (CFs). These discontinuities are thought to isolate between low-entropy, high-metallicity gas inside (i.e., below) the CF that was lifted from the center of the cluster by some radial factor f i and high-entropy, low-metallicity gas outside the CF that was pushed inward by a factor f o . We find broad support for such a picture, by comparing the entropy and metallicity discontinuities with the respective azimuthal averages, using newly deprojected thermal profiles in clusters A2029, A2142, A2204, and Centaurus, supplemented by deprojected CFs from the literature. In particular, the mean advection factors f K and f Z , inferred from entropy and metallicity, respectively, strongly correlate ( ) with each other, consistent with large-scale advection. However, unlike sloshing simulations, in which the inside/outside phases are an inflow/outflow settling back to equilibrium after a violent perturbation, our results are more consistent with an outflow/inflow, with the fast, Mach gas inside the CF being a rapidly heated or mixed outflow, probably originating from the cD galaxy, and gas outside the CF being an , slowly cooling inflow. In particular, entropy indicates an outside advection factor f Ko that is approximately constant in all CFs, gauging the distance traversed by inflowing gas within a cooling time. In contrast, and vary considerably among clusters and strongly correlate ( ) with the virial mass, and , suggesting that each cluster sustains a quasi-steady spiral flow.

Convincing evidence for the Halperin-Lubensky-Ma effect at the N-SmA transition in alkyloxycyanobiphenyl binary mixtures via a high-resolution birefringence study.

We present new high-resolution experimental data for the temperature behavior of optical birefringence for a series of mixture of the liquid crystals octyloxycyanobiphenyl (8OCB) and nonyloxycyanobiphenyl (9OCB) by using a rotating analyzer technique. The birefringence data have been used to probe the temperature dependence of the nematic order parameter [Formula: see text]. We have then arrived at values for possible entropy discontinuities at the nematic-smectic A transition temperature [Formula: see text] from the detailed inspection of [Formula: see text] data in the immediate vicinity of [Formula: see text]. The 9OCB mole fraction dependence of the obtained reduced entropy discontinuities has been shown to be well fitted with a crossover function which is itself consistent with the mean-field free energy expression with a non-zero cubic term arising from the Halperin-Lubensky-Ma (HLM) coupling. The obtained results are in good accordance with existing results from adiabatic scanning calorimetry (ASC). Our birefringence results and determined entropy discontinuities (consistent with calorimetry results) are in striking contrast with the recent birefringence results of Barman et al. (Phase Transit. 91, 58 (2018) published online 16 Aug. 2017) claiming second-order nematic-to-smectic A transitions for all mixtures. In this paper we present a possible explanation for this discrepancy. We have also extracted the effective critical exponent values [Formula: see text] characterizing the critical fluctuations near the N-SmA transition for all compositions by using the fact that the temperature derivative of the order parameter [Formula: see text] near [Formula: see text] exhibits the same power-law divergence as the specific heat capacity. Measurable latent heat values were extracted from optical birefringence data for mole fractions of 9OCB where the [Formula: see text] values are as low as 0.2, which is substantially lower than the tricritical value [Formula: see text]. This is qualitatively different from what has been observed so far in other liquid-crystal systems. Together with ASC data, these pecuilarities of the 8OCB+9OCB system render further convincing evidence for the presence of the HLM coupling effect at the N-SmA transition phase transition line.

Lagrangian particle method for compressible fluid dynamics

A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface/multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremal points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free interfaces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order. The method is generalizable to coupled hyperbolic–elliptic systems. Numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.

Test of Halperin-Lubensky-Ma crossover function at theN–Sm−Atransition in liquid crystal binary mixtures via high-resolution birefringence measurements

We report optical birefringence data for a series of mixtures of the liquid crystals octylcyanobiphenyl (8CB) and decylcyanobiphenyl (10CB). Nematic order parameter S data in the nematic and smectic A phases have been derived from phase angle changes obtained in temperature scans with a rotating analyzer method. These S values have been used to arrive at values for possible entropy discontinuities at the smectic A to nematic phase transition temperature T_{NA}. The 10CB mole fraction dependence of the obtained entropy discontinuities could be well fitted with a crossover function consistent with the mean-field free-energy expression with a nonzero cubic term arising from the coupling between the smectic-A order parameter and the orientational order parameter director fluctuations in the Halperin-Lubensky-Ma theory. The obtained results are in good agreement with existing results from adiabatic scanning calorimetry. By exploiting the fact that the temperature derivative of the order parameter S(T) near T_{NA} exhibits the same power law divergence as the specific heat capacity, we have extracted the effective critical exponent α values for the compositions under study. The critical exponent α has been observed to reach the tricritical value α_{TCP}=0.5 for the 10CB mole fraction of x=0.330.

Thermodynamic description of the liquid metals at pulsed energy flows impact

Here we suggest semiempirical equations of state defining the behavior of some solid metals at pulsed energy flows impact. A new wide-range two-phase equation of state of metals is proposed. These equations have few free parameters. They are estimated for Na and Cu. Melting curves of metals are defined within both one-phase approximation using Lindeman criterion, and two-phase-approximation. Volume and entropy discontinuities are calculated as a function of pressure at melting curve for Na and Cu. We also compared all the simulations results to the available experimental data for these metals.

SPHGal: smoothed particle hydrodynamics with improved accuracy for galaxy simulations

We present the smoothed-particle hydrodynamics implementation SPHGal, which combines some recently proposed improvements in GADGET. This includes a pressure-entropy formulation with a Wendland kernel, a higher order estimate of velocity gradients, a modified artificial viscosity switch with a modified strong limiter, and artificial conduction of thermal energy. With a series of idealized hydrodynamic tests we show that the pressure-entropy formulation is ideal for resolving fluid mixing at contact discontinuities but performs conspicuously worse at strong shocks due to the large entropy discontinuities. Including artificial conduction at shocks greatly improves the results. In simulations of Milky Way like disk galaxies a feedback-induced instability develops if too much artificial viscosity is introduced. Our modified artificial viscosity scheme prevents this instability and shows efficient shock capturing capability. We also investigate the star formation rate and the galactic outflow. The star formation rates vary slightly for different SPH schemes while the mass loading is sensitive to the SPH scheme and significantly reduced in our favored implementation. We compare the accretion behavior of the hot halo gas. The formation of cold blobs, an artifact of simple SPH implementations, can be eliminated efficiently with proper fluid mixing, either by conduction and/or by using a pressure-entropy formulation.

Estimation of entropy change at the first order martensitic transition in Ni–Mn–X based ferromagnetic shape memory alloys

Change in entropy (ΔS) has been estimated at the first order martensitic transition in selected Ni–Mn–X (Ga, Sn, and In) based ferromagnetic shape memory alloys (FSMAs). During the first-order martensitic structural phase transition, discontinuity in entropy leads to a large ΔS. ΔS can be estimated from differential scanning calorimeter curves. Magnetic characterization reveals that the magnetic contribution ∆SM, is dominant contributor to ΔS. ∆SM is also responsible for the giant magnetocaloric effect observed in these FSMAs. By controlling the valence electron to atom ratio (e/a), it is possible to realize a large entropy change near ambient temperature in these alloys. Estimation of ∆S and ∆SM in a variety of promising FSMAs provides a means to identify alloys suitable for applications such as magnetic sensors, actuators and magnetic refrigeration.

Response to “Comment on ‘Experimental evidence for excess entropy discontinuities in glass-forming solutions”’ [J. Chem. Phys. 139, 047101 (2013)

First Page

Experimental evidence for excess entropy discontinuities in glass-forming solutions

Glass transition temperatures T(g) are investigated in aqueous binary and multi-component solutions consisting of citric acid, calcium nitrate (Ca(NO(3))(2)), malonic acid, raffinose, and ammonium bisulfate (NH(4)HSO(4)) using a differential scanning calorimeter. Based on measured glass transition temperatures of binary aqueous mixtures and fitted binary coefficients, the T(g) of multi-component systems can be predicted using mixing rules. However, the experimentally observed T(g) in multi-component solutions show considerable deviations from two theoretical approaches considered. The deviations from these predictions are explained in terms of the molar excess mixing entropy difference between the supercooled liquid and glassy state at T(g). The multi-component mixtures involve contributions to these excess mixing entropies that the mixing rules do not take into account.

New type of phase transition in Reissner Nordström–AdS black hole and its thermodynamic geometry

The phase transition of a RN–AdS black hole is studied in details using Ehrenfest's equations. There is no discontinuity in entropy which signals a lack of any first order phase transition. We then show that although Ehrenfest's first equation is satisfied, the second is not, so that a true second order phase transition is also ruled out. However this deviation from the second Ehrenfest's equation, for a certain range of the black hole charge, indicates the existence of a new glassy type transition. We finally study the thermodynamic behaviour using state space geometry and find that the scalar curvature diverges exactly at those points where the heat capacity diverges.

First-order character of the smectic-A to chiral nematic transition in chiral liquid-crystal mixtures.

An investigation into the smectic-A to chiral nematic (N'A) transition in liquid crystals is presented by using adiabatic scanning calorimetry (ASC). It is predicted theoretically that chirality drives this transition to first order. This transition is studied in mixtures of the nonchiral liquid crystal octyloxycyanobiphenyl (8OCB) and the chiral 4-(2-methylbutyl)-4(')-cyanobiphenyl (CB15), a system with a large (chiral) nematic region that widens upon increasing the chiral (CB15) fraction. An ASC measurement on pure 8OCB showed no evidence for a latent heat, in agreement with previous ac calorimetric studies, with an upper boundary for the latent heat (if any) of 1.8 J/kg. Since pure 8OCB has no measurable latent heat, and taking into account the widening of the chiral nematic region, the possibility of a continuous to first-order crossover due to the coupling of the nematic and the smectic order parameters, as occurring in several cases of smectic-A to nematic (NA) transitions, can be excluded. However, for all examined mixtures a latent heat could be determined at the smectic-A to chiral nematic transition. This confirms theoretical predictions of the first order character of this transition. Quantitatively, theoretical predictions of the evolution of the entropy discontinuities and latent heats of this transition were not consistent with the experimental results. It was further observed that the transition temperature decreases linearly in agreement with theoretical predictions and a previous ac calorimetric study. Finally, it was observed that the pretransitional specific heat capacity shows an interesting evolution upon increasing chiral fraction, and it may be concluded that any theoretical model based on Landau theory is not sufficient to describe this transition.

A phase transition in H2O due to electrostriction pressure

It is predicted that water at ambient conditions should undergo a phase transition to a dense phase of H2O at a transition value Πt of the local electrostriction pressure. The transition is accompanied by a latent heat as well as discontinuity in entropy and electric field. The values of the field in which recent X-ray scattering at a charged RuO2/water interface revealed phase transitions to very dense ordered H2O layers are met without adjustable parameters. The latent heat has been observed earlier at a Hg/aqueous electrolyte interface. An attempt at an explanation of the hydration of Sr2+ ions is undertaken.

Angular dependence of the latent heat of vortex-lattice melting in untwinnedYBa2Cu3O7−δ

We measured the latent heat of vortex-lattice melting for varying angles \ensuremath{\Theta} between the external magnetic field H and the c axis of an untwinned ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ single crystal. The discontinuity in entropy at melting, $\ensuremath{\Delta}S$ per unit volume of sample, depends solely on the temperature T where melting occurs, but does not depend on \ensuremath{\Theta} and the corresponding melting field ${H}_{m}(T,\ensuremath{\Theta}).$ The T dependence of $\ensuremath{\Delta}S$ near the critical temperature ${T}_{c}$ can be quantitatively explained by a recently developed theory based on the London model that accounts for the strong T dependence of the model parameters near ${T}_{c}.$

Spin-wave velocity, entropy, and magnetization in bcc solid 3He.

Precise measurements of the [sup 3]He melting pressure in several magnetic fields have been made through the various magnetic ordering transitions. Throughout the low-field phase, we find a [ital T][sup 4] temperature dependence of the melting pressure, characteristic of antiferromagnetic spin waves with linear dispersion and a velocity of 7.8 cm/s, almost independent of field. However, the melting pressure in the high-field phase (HFP) deviates from the [ital T][sup 4] dependence near the HFP-paramagnetic phase transition, resulting in a very rapid entropy change near [ital T][sub [ital c]]. The spin-wave velocity increases with field, consistent with a strong temperature dependence of the magnetization. The entropy and magnetization discontinuities across the various phase boundaries have been determined. All results are thermodynamically consistent with the measured magnetic phase diagram.

Melting pressure of solid 3He through the magnetic-ordering transitions.

Magnetic ordering in solid $^{3}\mathrm{He}$ has been studied by measuring the melting pressure through the various phase transitions. We find a discontinuity in entropy at the high-field--paramagnetic phase transition at low fields, indicating that it is first order. The entropy discontinuity decreases as the field increases and the transition broadens, becoming second order above a field of about 0.65 T. The first precise determination of the first-order phase boundaries has been made, from which thermodynamic data not previously available are obtained.

Thermodynamic measurements in magnetically ordered solid3He

Measurements of the melting pressure and constant-volume pressure of solid3He have been made in the vicinity of the various magnetic-ordering transitions. Data have been obtained at several magnetic fields for both the low-field phase and the high-field phase, with particular attention given to the region of the polycritical point. The absence of a latent heat indicates that the transition from the paramagnetic to the high-field phase is second order or λ type. A spin-wave velocity of 6.95 cm/sec was obtained from theT4 temperature dependence of the melting pressure in the high-field phase forB=0.495 T. These data provide the entropy and volume discontinuities as functions of field along the first-order low-field phase boundary. The volume dependence of the transition temperatures has been extracted from these and other data.

Microscopic Description of Nematic-Smectic A2 and Nematic-Smectic A1-Smectic A2 Phase Transitions in Binary Mixture of Polar and Nonpolar Liquid Crystals

Abstract In the present paper, in a mean field approximation, we considered binary mixtures of polar and nonpolar liquid crystals (LC) with ideal orientational order. It is assumed that nonpolar molecules can form only monolayer smectic A-structure whereas polar molecules can form both monolayer smectic A-structure with short-range antiferroelectric order and bilayer smectic A-structure with long-range antiferroelectric order. By analogy with McMillan's theory the self-consistent equations determining order parameters for these smectic A structures are introduced. It is shown that smectic A1 phase with monolayer smectic A structure and smectic A2 phase with coexisting monolayer and bilayer smectic-A structures can ocur in the mixture. Phase diagram for mixture and entropy discontinuities at the nematic-smectic A1 and smectic A1-smectic A2 phase transitions obtained by numerical solution of self-consistent equations are similar to experimental ones. Also the temperature and concentration dependences of int...

Phenomenology of first-order phase transitions

A phenomenological description of first-order phase transitions is proposed in terms of the solution of a certain linear, first-order, partial differential equation suggested by Fisher. In the asymptotic region of the critical point, the coefficient functions of the equation are uniquely determined by the scaling laws. The imposition of the further requirement that the phase boundary coincide with a characteristic curve of this equation is shown to lead to solutions that can reproduce the singular behavior\char22{}for example, the density and entropy discontinuities for the case of the liquid-gas transition\char22{}along the entire vapor-pressure curve. The important role played by the characteristic curves is stressed and confirmed for the special case of the ideal, $d$-dimensional, Bose gas. New relations involving discontinuities in the second derivatives of the thermodynamic functions are derived and shown to be useful in obtaining the coefficient functions near the phase boundary. Details are presented for the case of ferromagnetic and ferroelectric systems and include a comparison with experiment.