Thermodynamic Response Functions Research Articles

Optimizing Work Extraction in the Presence of an Entropic Potential: An Entropic Stochastic Resonance.

We study the nontrivial thermodynamic responses of an overdamped Brownian system driven by an unbiased driving force when the particle is confined inside a bilobal irregular structure. The spatial irregularity of the confinement results in an effective entropic bistable potential along the direction of transport. We calculate the thermodynamic response functions in terms of the averaged work done and the absorbed heat over a cycle of driving. We find that the thermodynamic responses are influenced by the nonlinearity of the effective entropic potential, the frequency of the external periodic driving force, and the random thermal fluctuations in a nontrivial way. In the presence of an optimal amount of thermal noise and a favoring driving frequency, the process exhibits a resonance-like precedent in terms of both output work and absorbed heat. We explore the conditions to get best synchronized work extraction (or absorbed heat), which can be utilized as a potential quantifier of an entropic stochastic resonance phenomenon. Finally, we identify a hallmark of entropy dominance over an analogous energy-driven scenario in terms of output work.

Converging Periodic Boundary Conditions and Detection of Topological Gaps on Regular Hyperbolic Tessellations.

Tessellations of the hyperbolic spaces by regular polygons support discrete quantum and classical models with unique spectral and topological characteristics. Resolving the true bulk spectra and the thermodynamic response functions of these models requires converging periodic boundary conditions and our Letter delivers a practical and rigorous solution for this open problem on generic {p,q}-tessellations. This enables us to identify the true spectral gaps of bulk Hamiltonians and construct all but one topological models that deliver the topological gaps predicted by the K theory of the lattices. We demonstrate the emergence of the expected topological spectral flows whenever two such bulk models are deformed into each other and prove the emergence of topological channels whenever a soft physical interface is created between different topological classes of Hamiltonians.

Thermodynamic response functions and Stokes-Einstein breakdown in superheated water under gigapascal pressure

Thermodynamic response functions and Stokes-Einstein breakdown in superheated water under gigapascal pressure

Supercritical fluids behave as complex networks

Supercritical fluids play a key role in environmental, geological, and celestial processes, and are of great importance to many scientific and engineering applications. They exhibit strong variations in thermodynamic response functions, which has been hypothesized to stem from the microstructural behavior. However, a direct connection between thermodynamic conditions and the microstructural behavior, as described by molecular clusters, remains an outstanding issue. By utilizing a first-principles-based criterion and self-similarity analysis, we identify energetically localized molecular clusters whose size distribution and connectivity exhibit self-similarity in the extended supercritical phase space. We show that the structural response of these clusters follows a complex network behavior whose dynamics arises from the energetics of isotropic molecular interactions. Furthermore, we demonstrate that a hidden variable network model can accurately describe the structural and dynamical response of supercritical fluids. These results highlight the need for constitutive models and provide a basis to relate the fluid microstructure to thermodynamic response functions.

Manifestations of the structural origin of supercooled water's anomalies in the heterogeneous relaxation on the potential energy landscape.

Liquid water is well-known for its intriguing thermodynamic anomalies in the supercooled state. The phenomenological two-state models-based on the assumption of the existence of two types of competing local states (or, structures) in liquid water-have been extremely successful in describing water's thermodynamic anomalies. However, the precise structural features of these competing local states in liquid water still remain elusive. Here, we have employed a predefined structural order parameter-free approach to unambiguously identify two types of competing local states-entropically and energetically favored-with significantly different structural and energetic features in the TIP4P/2005 liquid water. This identification is based on the heterogeneous structural relaxation of the system in the potential energy landscape (PEL) during the steepest-descent energy minimization. This heterogeneous relaxation is characterized using order parameters inspired by the spin-glass transition in frustrated magnetic systems. We have further established a direct relationship between the population fluctuation of the two states and the anomalous behavior of the heat capacity in supercooled water. The composition-dependent spatial distribution of the entropically favored local states shows an interesting crossover from a spanning network-like single cluster to the spatially delocalized clusters in the close vicinity of the Widom line. Additionally, this study establishes a direct relationship between the topographic features of the PEL and the water's thermodynamic anomalies in the supercooled state and provides alternate markers (in addition to the locus of maxima of thermodynamic response functions) for the Widom line in the phase plane.

Destabilization of binary mixing layer in supercritical conditions

Compressible mixing layer instabilities are of importance to a wide range of environmental and industrial applications. Past studies have focused on either ideal-gas or real-fluid thermodynamic regimes of single-species mixing layers. However, mixing layers of binary mixtures at supercritical conditions, commonly encountered in fuel injection systems, introduce additional complexities due to the added compositional degree-of-freedom. Moreover, the effect of strong variations in thermodynamic response functions across the Widom line on the binary mixing layer stability remains poorly understood. Thus, the objective of this study is to examine the coupling between the hydrodynamic instability and the real-fluid thermodynamics across the Widom line and its effects on the overall binary mixing layer dynamics. To this end, we develop a linear stability analysis of the full binary-species compressible transport equations coupled with the PC-SAFT equation of state. Analysis shows the existence of a novel instability mechanism that arises from juxtapositioning of the Widom-line transition and the hydrodynamic inflection point. This novel thermodynamically induced instability mechanism has the net effect of destabilizing the binary mixing layer at lowering supercritical conditions towards the critical pressure point. This is in contrast to previous stability analyses of supercritical single-species mixing layers, where increasing pressure destabilizes the flow due to its effect on reducing the density stratification. The discovered thermodynamically induced instability mechanism of binary mixing flows highlights the need for an extension of classical instability criteria to incorporate the effect of strong variations in the thermodynamic response functions across the Widom line on mixing layer instability.

Widom line of supercritical CO2 calculated by equations of state and molecular dynamics simulation

Supercritical CO2 has been widely applied in power cycle owing to the exceptional physical property in the supercritical region. The Widom line is very important to reveal the pseudo-boiling mechanism of supercritical CO2 which plays significant influence on design and optimization of power cycle. In this paper, the Widom lines for supercritical CO2 in terms of thermodynamic response functions are constructed using equation of state (EoS) and molecular dynamics (MD) simulation. Different equations of state and CO2 models are proposed and applied to predict the various thermodynamic properties. The results show that the Peng-Robinson (PR) series equations of state play better performance in predicting the thermodynamic properties and the average absolute relative deviation is around 5.7 % compared to the NIST database. The TraPPE model could represent a very good agreement with the experimental values at different pressures with about 1~6 % deviation. Owing to large temperature interval for molecular dynamics, the simulated values could not capture the dramatic change of thermodynamic properties at low temperature region (295 ℃< T < 310 ℃), resulting in that the simulated thermodynamic properties by molecular dynamics are generally lower than that calculated by Peng-Robinson equation of state. When the temperature is larger 335 K, the deviation of Widom lines between the NIST and PR EoS decreases gradually with the temperature. Nonetheless, all the Widom lines could fall into the coexistence zone of liquid-like and gas-like phase which is surrounded by the isobaric temperature boundaries.

Origin of the anomalous properties in supercooled water based on experimental probing inside “no-man's land”

Austen Angell conducted pioneering work that opened up the field of supercooled water by observing the temperature dependent divergence of the thermodynamic response functions. Many different scenarios have been proposed as the origin of the anomalous properties and now it has become possible to test the various hypotheses in experimental studies of bulk supercooled water at conditions where ice crystallization becomes extremely rapid. Through the usage of x-ray lasers, ultrafast measurements could be conducted, as the sample is rapidly brought to the extreme conditions on time scales preceding ice formation. In particular the experimental observation of the existence of a liquid-liquid transition at positive pressure, one phase behavior at atmospheric conditions at temperatures down to 228 K, and the existence of maxima in several properties at 230 K indicative of a Widom line, are only consistent with the proposed liquid-liquid critical point model as the origin of the anomalous properties. • Unexpected behavior of the heat capacity started the field of supercooled water. • Experimental exploration of no-man's land tests hypotheses. • The liquid-liquid transition and critical point scenario consistent with the data.

Anomalies and Local Structure of Liquid Water from Boiling to the Supercooled Regime as Predicted by the Many-Body MB-pol Model.

For the past 50 years, researchers have sought molecular models that can accurately reproduce water's microscopic structure and thermophysical properties across broad ranges of its complex phase diagram. Herein, molecular dynamics simulations with the many-body MB-pol model are performed to monitor the thermodynamic response functions and local structure of liquid water from the boiling point down to deeply supercooled temperatures at ambient pressure. The isothermal compressibility and isobaric heat capacity show maxima near 223 K, in excellent agreement with recent experiments, and the liquid density exhibits a minimum at ∼208 K. A local tetrahedral arrangement, where each water molecule accepts and donates two hydrogen bonds, is found to be the most probable hydrogen-bonding topology at all temperatures. This work suggests that MB-pol may provide predictive capability for studies of liquid water's physical properties across broad ranges of thermodynamic states, including the so-called water's "no man's land" which is difficult to probe experimentally.

Structural and thermodynamic properties of inhomogeneous fluids in rectangular corrugated nano-pores

Based on the free-energy average method, an area-weighted effective potential is derived for rectangular corrugated nano-pore. With the obtained potential, classical density functional theory is employed to investigate the structural and thermodynamic properties of confined Lennard–Jones fluid in rectangular corrugated slit pores. Firstly, influence of pore geometry on the adsorptive potential is calculated and analyzed. Further, thermodynamic properties including excess adsorption, solvation force, surface free energy and thermodynamic response functions are systematically investigated. It is found that pore geometry can largely modulate the structure of the confined fluids, which in turn influences other thermodynamic properties. In addition, the results show that different geometric elements have different influences on the confined fluids. The work provides an effective route to investigate the effect of roughness on confined fluids. It is expected to shed light on further understanding about interfacial phenomena near rough walls, and then provide useful clues for the design and characterization of novel materials.

Dynamical spectral structure of density fluctuation near the QCD critical point

The expression for the dynamical spectral structure of the density fluctuation near the QCD critical point has been derived using linear response theory within the purview of Israel–Stewart relativistic viscous hydrodynamics. The change in the spectral structure of the system as it approaches the critical point has been studied. The effects of the critical point have been introduced in the system through a realistic equation of state and the scaling behaviour of various transport coefficients and thermodynamic response functions. We have found that the Rayleigh and Brillouin peaks are distinctly visible when the system is away from the critical point but the peaks tend to merge near the critical point. The sensitivity of the structure of the spectral function on wave vector (k) of the sound wave has been demonstrated. It has been shown that the Brillouin peaks get merged with the Rayleigh peak because of the absorption of sound waves in the vicinity of the critical point.

The fate of nonlinear perturbations near the QCD critical point

The impact of the QCD critical point on the propagation of nonlinear waves has been studied. The effects have been investigated within the scope of second-order causal dissipative hydrodynamics by incorporating the critical point into the equation of state, and the scaling behavior of transport coefficients and of thermodynamic response functions. Near the critical point, the nonlinear waves are found to be significantly damped which may result in the disappearance of the Mach cone effects of the away side jet. Such damping may lead to enhancement in the fluctuations of elliptic and higher flow coefficients. Therefore, the disappearance of Mach cone effects and the enhancement of fluctuations in flow harmonics in the event-by-event analysis may be considered as signals of the critical endpoint.

Interacting fermions in narrow-gap semiconductors with band inversion

Highly unconventional behavior of the thermodynamic response functions has been experimentally observed in a narrow gap semiconductor samarium hexaboride. Motivated by these observations, we use renormalization group technique to investigate many-body instabilities in the f-orbital narrow gap semiconductors with band inversion in the limit of weak coupling. By projecting out the double occupancy of the f-states we formulate a low-energy theory describing the interacting particles in two hybridized electron- and hole-like bands. The interactions are assumed to be weak and short-ranged. We take into account the difference between the effective masses of the quasiparticles in each band. Upon carrying out the renormalization group analysis we find that there is only one stable fixed point corresponding to the excitonic instability with time-reversal symmetry breaking for small enough mismatch between the effective masses.

Enhancement and maximum in the isobaric specific-heat capacity measurements of deeply supercooled water using ultrafast calorimetry

Knowledge of the temperature dependence of the isobaric specific heat (Cp) upon deep supercooling can give insights regarding the anomalous properties of water. If a maximum in Cp exists at a specific temperature, as in the isothermal compressibility, it would further validate the liquid-liquid critical point model that can explain the anomalous increase in thermodynamic response functions. The challenge is that the relevant temperature range falls in the region where ice crystallization becomes rapid, which has previously excluded experiments. Here, we have utilized a methodology of ultrafast calorimetry by determining the temperature jump from femtosecond X-ray pulses after heating with an infrared laser pulse and with a sufficiently long time delay between the pulses to allow measurements at constant pressure. Evaporative cooling of ∼15-µm diameter droplets in vacuum enabled us to reach a temperature down to ∼228 K with a small fraction of the droplets remaining unfrozen. We observed a sharp increase in Cp, from 88 J/mol/K at 244 K to about 218 J/mol/K at 229 K where a maximum is seen. The Cp maximum is at a similar temperature as the maxima of the isothermal compressibility and correlation length. From the Cp measurement, we estimated the excess entropy and self-diffusion coefficient of water and these properties decrease rapidly below 235 K.

Finite size effects around pseudo-transition in one-dimensional models with nearest neighbor interaction

Recently gigantic peaks in thermodynamic response functions have been observed at finite temperature for one-dimensional models with short-range coupling, closely resembling a second-order phase transition. Thus, we will analyze the finite temperature pseudo-transition property observed in some one-dimensional models and its relationship with finite size effect. In particular, we consider two chain models to study the finite size effects; these are the Ising-Heisenberg tetrahedral chain and an Ising-Heisenberg-type ladder model. Although the anomalous peaks of these one-dimensional models have already been studied in the thermodynamic limit, here we will discuss the finite size effects of the chain and why the peaks do not diverge in the thermodynamic limit. So, we discuss the dependence of the finite size effects, for moderately and sufficiently large systems, in which the specific heat and magnetic susceptibility exhibit peculiar rounded towering peaks for a given temperature. This behavior is quite similar to a continuous phase transition, but there is no singularity. For moderately large systems, the peaks narrow and increase in height as the number of unit cells is increased, and the location of peak shifts slightly. Hence, one can naively induce that the sharp peak should lead to a divergence in the thermodynamic limit. However, for a rather large system, the height of a peak goes asymptotically to a finite value. Our result rigorously confirms the dependence of the peak height with the number of unit cells at the pseudo-critical temperature. We also provide an alternative empirical function that satisfactorily fits specific heat and magnetic susceptibility at pseudo-critical temperature. Certainly, our result is crucial to understand the finite size correction behavior in quantum spin models, which in general are only numerically tractable within the framework of the finite size analysis.

The "isothermal" compressibility of active matter.

We demonstrate that the mechanically defined "isothermal" compressibility behaves as a thermodynamic-like response function for suspensions of active Brownian particles. The compressibility computed from the active pressure-a combination of the collision and unique swim pressures-is capable of predicting the critical point for motility induced phase separation, as expected from the mechanical stability criterion. We relate this mechanical definition to the static structure factor via an active form of the thermodynamic compressibility equation and find the two to be equivalent, as would be the case for equilibrium systems. This equivalence indicates that compressibility behaves like a thermodynamic response function, even when activity is large. Finally, we discuss the importance of the phase interface when defining an active chemical potential. Previous definitions of the active chemical potential are shown to be accurate above the critical point but breakdown in the coexistence region. Inclusion of the swim pressure in the mechanical compressibility definition suggests that the interface is essential for determining phase behavior.

Nuclear quantum effects on the thermodynamic, structural, and dynamical properties of water.

We perform path-integral molecular dynamics (PIMD) simulations of H2O and D2O using the q-TIP4P/F model. Simulations are performed at P = 1 bar and over a wide range of temperatures that include the equilibrium (T≥ 273 K) and supercooled (210 ≤T < 273 K) liquid states of water. The densities of both H2O and D2O calculated from PIMD simulations are in excellent agreement with experiments in the equilibrium and supercooled regimes. We also evaluate important thermodynamic response functions, specifically, the thermal expansion coefficient αP(T), isothermal compressibility κT(T), isobaric heat capacity CP(T), and static dielectric constant ε(T). While these properties are in excellent [αP(T) and κT(T)] or semi-quantitative agreement [CP(T) and ε(T)] with experiments in the equilibrium regime, they are increasingly underestimated upon further cooling. It follows that the inclusion of nuclear quantum effects in PIMD simulations of (q-TIP4P/F) water is not sufficient to reproduce the anomalous large fluctuations in density, entropy, and electric dipole moment characteristic of supercooled water. It has been hypothesized that water may exhibit a liquid-liquid critical point (LLCP) in the supercooled regime at P > 1 bar and that such a LLCP generates a maximum in CP(T) and κT(T) at 1 bar. Consistent with this hypothesis and in particular, with experiments, we find a maximum in the κT(T) of q-TIP4P/F light and heavy water at T≈ 230-235 K. No maximum in CP(T) could be detected down to T≥ 210 K. We also calculate the diffusion coefficient D(T) of H2O and D2O using the ring-polymer molecular dynamics (RPMD) technique and find that computer simulations are in remarkable good agreement with experiments at all temperatures studied. The results from RPMD/PIMD simulations are also compared with the corresponding results obtained from classical MD simulations of q-TIP4P/F water where atoms are represented by single interacting sites. Surprisingly, we find minor differences in most of the properties studied, with CP(T), D(T), and structural properties being the only (expected) exceptions.

Magnetic properties of spin-[formula omitted] Blume-Capel chain under a magnetic field

A magnetic property of the one dimensional spin-7/2 Blume-Capel model under the magnetic field has been investigated by means of transfer matrix method. Thermodynamic response functions are also obtained for varying values of reduced thermodynamic temperature and scaling magnetic field. We have seen that the crystal field strongly affects magnetic plateau mechanism. Our simulation results demonstrate that the plateau becomes smoother when the value of the temperature increased. Entropy of the system goes to zero rapidly for positive crystal field values so we see only saturation values of the system. We observed that the minimum of specific heat tends to shift to the relatively lower thermodynamic temperature regions as the strength of the crystal field is increased.

Fluid injection with supercritical reservoir conditions: Overview on morphology and mixing

The present work provides an overview on the possible phase transitions associated with supercritical fluid injection and a detailed evaluation of the mixing process between injectant fluid and quiescent ambience. The experiments cover superheated liquid disintegration, pseudo-boiling transition and single-phase jets under different nozzle pressure ratios. Pseudo-boiling effects emerge when rapid, subsequent changes in pressure/temperature interact with the non-linear behavior of thermodynamic response functions across the Widom line. The associated density fluctuations cause a significant increase in the scattering cross section and may lead to thermo-convective instabilities. Our analysis of the mixing process demonstrates the limited applicability of the adiabatic mixing model, which is often restricted to short residence times even in highly turbulent jets (Re=O(105)). Specifically, our findings show the importance of considering all coupled transport processes in the analysis of mixing problems at high pressures, in particular in presence of large mass concentration and temperature gradients.

Some Aspects of the Liquid Water Thermodynamic Behavior: From The Stable to the Deep Supercooled Regime.

Liquid water is considered to be a peculiar example of glass forming materials because of the possibility of giving rise to amorphous phases with different densities and of the thermodynamic anomalies that characterize its supercooled liquid phase. In the present work, literature data on the density of bulk liquid water are analyzed in a wide temperature-pressure range, also including the glass phases. A careful data analysis, which was performed on different density isobars, made in terms of thermodynamic response functions, like the thermal expansion and the specific heat differences , proves, exclusively from the experimental data, the thermodynamic consistence of the liquid-liquid transition hypothesis. The study confirms that supercooled bulk water is a mixture of two liquid “phases”, namely the high density (HDL) and the low density (LDL) liquids that characterize different regions of the water phase diagram. Furthermore, the isobars behaviors clearly support the existence of both a liquid–liquid transition and of a liquid–liquid critical point.