Ensemble-averaged Values Research Articles

Temperature fluctuations in a relativistic gas: Pressure corrections and possible consequences in the deconfinement transition

In this work, we study the effects of random temperature fluctuations on the partition function of a quantum system by means of the . This picture provides a conceptual model for a quantum nonequilibrium system, depicted as an ensemble of subsystems at different temperatures, randomly distributed with respect to a given mean value. We then assume the temperature displays stochastic fluctuations T=T0+δT with respect to its ensemble average value T0, with zero mean δT¯=0 and standard deviation δT2¯=Δ. By means of the replica method, we obtain the average grand canonical potential, leading to the equation of state and the corresponding excess pressure caused by these fluctuations with respect to the equilibrium system at a uniform temperature. Our findings reveal an increase in pressure as the system’s ensemble average temperature T0 rises, consistently exceeding the pressure observed in an equilibrium state. We applied our general formalism to three paradigmatic physical systems; the relativistic Fermi gas, the ideal gas of photons, and a gas of non-Abelian gauge fields (gluons) in the noninteracting limit. Finally, we explore the implications for the deconfinement transition in the context of the simple bag model, where we show that the critical temperature decreases. Published by the American Physical Society 2024

ISIT-QA: In Silico Imaging Trial to Evaluate a Low-Count Quantitative SPECT Method Across Multiple Scanner-Collimator Configurations for 223Ra-Based Radiopharmaceutical Therapies.

Personalized dose-based treatment planning requires accurate and reproducible noninvasive measurements to ensure safety and effectiveness. Dose estimation using SPECT is possible but challenging for alpha (α)-particle-emitting radiopharmaceutical therapy (α-RPT) because of complex γ-emission spectra, extremely low counts, and various image-degrading artifacts across a plethora of scanner-collimator configurations. Through the incorporation of physics-based considerations and skipping of the potentially lossy voxel-based reconstruction step, a recently developed projection-domain low-count quantitative SPECT (LC-QSPECT) method has the potential to provide reproducible, accurate, and precise activity concentration and dose measures across multiple scanners, as is typically the case in multicenter settings. To assess this potential, we conducted an in silico imaging trial to evaluate the LC-QSPECT method for a 223Ra-based α-RPT, with the trial recapitulating patient and imaging system variabilities. Methods: A virtual imaging trial titled In Silico Imaging Trial for Quantitation Accuracy (ISIT-QA) was designed with the objectives of evaluating the performance of the LC-QSPECT method across multiple scanner-collimator configurations and comparing performance with a conventional reconstruction-based quantification method. In this trial, we simulated 280 realistic virtual patients with bone-metastatic castration-resistant prostate cancer treated with 223Ra-based α-RPT. The trial was conducted with 9 simulated SPECT scanner-collimator configurations. The primary objective of this trial was to evaluate the reproducibility of dose estimates across multiple scanner-collimator configurations using LC-QSPECT by calculating the intraclass correlation coefficient. Additionally, we compared the reproducibility and evaluated the accuracy of both considered quantification methods across multiple scanner-collimator configurations. Finally, the repeatability of the methods was evaluated in a test-retest study. Results: In this trial, data from 268 223RaCl2 treated virtual prostate cancer patients, with a total of 2,903 lesions, were used to evaluate LC-QSPECT. LC-QSPECT provided dose estimates with good reproducibility across the 9 scanner-collimator configurations (intraclass correlation coefficient > 0.75) and high accuracy (ensemble average values of recovery coefficients ranged from 1.00 to 1.02). Compared with conventional reconstruction-based quantification, LC-QSPECT yielded significantly improved reproducibility across scanner-collimator configurations, accuracy, and test-retest repeatability ([Formula: see text] Conclusion: LC-QSPECT provides reproducible, accurate, and repeatable dose estimations in 223Ra-based α-RPT as evaluated in ISIT-QA. These findings provide a strong impetus for multicenter clinical evaluations of LC-QSPECT in dose quantification for α-RPTs.

Uncertainty quantification of the diffuse sound field assumption in sound insulation predictions

The transmission loss of a partition depends on the sound fields in the adjoining rooms, which are often taken to be diffuse. A diffuse sound field is a random field, representing a conceptual ensemble of rooms with the same volume and reverberation time, but otherwise any possible arrangement of boundaries and small objects that have a wave scattering effect. Uncertainty due to random wave scattering is therefore inherently present in diffuse transmission loss values. In this work, closed-form expressions are presented for quantifying this uncertainty, such that it becomes possible to estimate by how much the transmission loss of a particular room-wall-room system may deviate from the nominal, ensemble average value which corresponds to omnidirectional incidence and halfspace radiation. The first expression is exact yet its evaluation requires knowledge of the dynamic stiffness of the partitioning structure and of the radiation impedances of the surrounding fluids. The second expression is approximate and depends on energetic quantities only, so it is also applicable in an experimental setting. The expressions are validated in a Monte-Carlo simulation study involving a single wall.

Orientation distributions of vacuum-deposited organic emitters revealed by single-molecule microscopy

The orientation of luminescent molecules in organic light-emitting diodes strongly influences device performance. However, our understanding of the factors controlling emitter orientation is limited as current measurements only provide ensemble-averaged orientation values. Here, we use single-molecule imaging to measure the transition dipole orientation of individual emitter molecules in a state-of-the-art thermally evaporated host and thereby obtain complete orientation distributions of the hyperfluorescence-terminal emitter C545T. We achieve this by realizing ultra-low doping concentrations (10−6 wt%) of C545T and minimising background levels to reliably measure its photoluminescence. This approach yields the orientation distributions of >1000 individual emitter molecules in a system relevant to vacuum-processed devices. Analysis of solution- and vacuum-processed systems reveals that the orientation distributions strongly depend on the nanoscale environment of the emitter. This work opens the door to attaining unprecedented information on the factors that determine emitter orientation in current and future material systems for organic light-emitting devices.

Drop Interactions with the Conical Shock Structure Generated by a Mach 4.5 Projectile

This work presents measurements of liquid drop deformation and breakup time behind approximately conical shock waves and evaluates the predictive capabilities of low-order models and correlations developed using planar shock experiments. A conical shock was approximated by firing a bullet at Mach 4.5 past a vertical column of water drops with a mean initial diameter of . The time-resolved drop position and maximum transverse dimension were characterized using backlit stereo images taken at 500 kHz. The gas density and velocity fields experienced by the drops were estimated using a Reynolds-averaged Navier–Stokes simulation of the bullet. Classical correlations predict drop breakup times and deformation in error by a factor of 3 or more. The Taylor analogy breakup (TAB) model predicts deformed drop diameters that agree within the confidence bounds of the ensemble-averaged experimental values using a dimensionless constant compared to the accepted value . Results demonstrate existing correlations are inadequate for predicting the drop response to the three-dimensional relaxation of the flowfield downstream of a conical-like shock and suggest the TAB model results represent a path toward improved predictions.

Solvable model of deep thermalization with distinct design times

We study the emergence over time of a universal, uniform distribution of quantum states supported on a finite subsystem, induced by projectively measuring the rest of the system. Dubbeddeep thermalization, this phenomenon represents a form of equilibration in quantum many-body systems stronger than regular thermalization, which only constrains the ensemble-averaged values of observables. While there exist quantum circuit models of dynamics in one dimension where this phenomenon can be shown to arise exactly, these are special in that deep thermalization occurs at precisely the same time as regular thermalization. Here, we present an exactly-solvable model of chaotic dynamics where the two processes can be shown to occur over different time scales. The model is composed of a finite subsystem coupled to an infinite random-matrix bath through a small constriction, and highlights the role of locality and imperfect thermalization in constraining the formation of such universal wavefunction distributions. We test our analytical predictions against exact numerical simulations, finding excellent agreement.

Uncertainty quantification of diffuse sound insulation values

The sound transmission loss of a partitioning structure depends on the nature of the sound fields in the source and receiver spaces. In an indoor setting, both sound fields are often taken to be diffuse. A diffuse field may represent the sound field of a conceptual ensemble of rooms with the same volume and reverberation time, but otherwise any possible arrangement of boundaries and small objects that have a wave scattering effect. Uncertainty due to random wave scattering is therefore inherently present in the diffuse transmission loss values. In this paper, closed-form expressions are derived for quantifying this uncertainty, such that it becomes possible to estimate by how much the transmission loss of a particular room–wall–room system may deviate from the nominal, ensemble-averaged diffuse value which corresponds to omni-directional incidence and halfspace radiation. First, an exact expression is derived for the harmonic or band-averaged diffuse transmission loss variance, based on hybrid deterministic–statistical energy analysis theory. Its evaluation requires knowledge of the dynamic stiffness of the partitioning structure and of the radiation impedances of the surrounding fluids. Subsequently, an approximate expression is derived, which depends on energy-related quantities only, making it also applicable in an experimental setting. Furthermore, it is demonstrated that the diffuse transmission loss is approximately normally distributed, such that a complete uncertainty quantification is possible from the mean and variance values. The expressions are verified in a Monte-Carlo simulation study involving a single wall and then validated with experimental data of double-leaf plasterboard walls containing flexible steel studs.

An ensemble-based decision workflow for reservoir management

It is challenging to make optimal field development and reservoir management decisions with diminishing resources and low-emission requirements. For an optimal exploitation of the reservoir fluids, it is necessary to introduce advanced digital tools and account for geological uncertainty when making decisions. This paper discusses an ensemble-based probabilistic decision-making workflow for closed-loop reservoir management. The reservoir model is a synthetic but realistic model with oil, gas, and water. We show how to use ensemble methods in a workflow for integrated uncertainty prediction, history matching, and robust optimization. The workflow uses advanced ensemble-based history-matching techniques to update a reservoir model in the annual maturation process. After the history-matching update, an optimization process decides the best wells to drill next to gain the highest net present value. An additional robust decision step evaluates the wells over the ensemble of reservoir models to ensure they lead to a positive ensemble-averaged net present value. The approach allows for up-to-date predictions, including uncertainty estimates, leading to improved decision support for field development, well-planning, production strategies, and reservoir management.

Inner Flame Front Structures and Burning Velocities of Premixed Turbulent Planar Ammonia/Air and Methane/Air Flames

Ammonia (mathrm {NH_3}) has attracted interest as a future carbon-free synthetic fuel due to its economic storage and transportation. In this study, quasi direct numerical simulations (quasi-DNS) with detailed-chemistry have been performed in 3-D to examine the flame thickness and assess the validity of Damköhler’s first hypothesis for premixed turbulent planar ammonia/air and methane/air flames under different turbulence levels. The Karlovitz number is systematically changed from 4.26 to 12.06 indicating that all the test conditions are located within the thin reaction zones combustion regime. Results indicate that the ensemble average values of the preheat zone thickness deviate slightly from the thin laminar flamelet assumption, while the reaction zone regions remain relatively intact. Following the balance equation of reaction progress variable gradient, normal strain rate and the tangential diffusion component of flame displacement speed variation in the normal direction to the flame surface are found to be responsible for thickening the flame. However, the sum of reaction and normal diffusion components of flame displacement speed variation in the normal direction to the flame surface is in charge of flame thinning for ammonia/air and methane/air flames. In addition, the validity of Damköhler’s first hypothesis is confirmed by indicating that the ratio of the turbulent burning velocity to the unstrained premixed laminar burning velocity is relatively equal to the ratio of the wrinkled to the unwrinkled flame surface area. Furthermore, the probability density functions of the density-weighted flame displacement speed show that the bulk of flame elements propagate identical to the unstrained premixed laminar flame.

Quantification of a Neurological Protein in a Single Cell Without Amplification.

Proteins are key biomolecules that not only play various roles in the living body but also are used as biomarkers. If these proteins can be quantified at the level of a single cell, understanding the role of proteins will be deepened and diagnosing diseases and abnormality will be further upgraded. In this study, we quantified a neurological protein in a single cell using atomic force microscopy (AFM). After capturing specifically disrupted-in-schizophrenia 1 (DISC1) in a single cell onto a microspot immobilizing the corresponding antibody on the surface, force mapping with AFM was followed to visualize individual DISC1. Although a large variation of the number of DISC1 in a cell was observed, the average number is 4.38 × 103, and the number agrees with the ensemble-averaged value. The current AFM approach for the quantitative analysis of proteins in a single cell should be useful to study molecular behavior of proteins in depth and to follow physiological change of individual cells in response to external stimuli.

Jamming in confined geometry: Criticality of the jamming transition and implications of structural relaxation in confined supercooled liquids* *Project supported by the National Natural Science Foundation of China (Grant No. 11734014).

In marginally jammed solids confined by walls, we calculate the particle and ensemble averaged value of an order parameter, 〈Ψ(r)〉, as a function of the distance to the wall, r. Being a microscopic indicator of structural disorder and particle mobility in solids, Ψ is by definition the response of the mean square particle displacement to the increase of temperature in the harmonic approximation and can be directly calculated from the normal modes of vibration of the zero-temperature solids. We find that, in confined jammed solids, 〈Ψ(r)〉 curves at different pressures can collapse onto the same master curve following a scaling function, indicating the criticality of the jamming transition. The scaling collapse suggests a diverging length scale and marginal instability at the jamming transition, which should be accessible to sophisticatedly designed experiments. Moreover, 〈Ψ(r)〉 is found to be significantly suppressed when approaching the wall and anisotropic in directions perpendicular and parallel to the wall. This finding can be applied to understand the r-dependence and anisotropy of the structural relaxation in confined supercooled liquids, providing another example of understanding or predicting behaviors of supercooled liquids from the perspective of the zero-temperature amorphous solids.

Massively parallel classical logic via coherent dynamics of an ensemble of quantum systems with dispersion in size

Quantum parallelism can be implemented on a classical ensemble of discrete level quantum systems. The nanosystems are not quite identical, and the ensemble represents their individual variability. An underlying Lie algebraic theory is developed using the closure of the algebra to demonstrate the parallel information processing at the level of the ensemble. The ensemble is addressed by a sequence of laser pulses. In the Heisenberg picture of quantum dynamics the coherence between the N levels of a given quantum system can be handled as an observable. Thereby there are N2 logic variables per N level system. This is how massive parallelism is achieved in that there are N2 potential outputs for a quantum system of N levels. The use of an ensemble allows simultaneous reading of such outputs. Due to size dispersion the expectation values of the observables can differ somewhat from system to system. We show that for a moderate variability of the systems one can average the N2 expectation values over the ensemble while retaining closure and parallelism. This allows directly propagating in time the ensemble averaged values of the observables. Results of simulations of electronic excitonic dynamics in an ensemble of quantum dot (QD) dimers are presented. The QD size and interdot distance in the dimer are used to parametrize the Hamiltonian. The dimer N levels include local and charge transfer excitons within each dimer. The well-studied physics of semiconducting QDs suggests that the dimer coherences can be probed at room temperature.

Band-Limited Reference-Free Speckle Spectroscopy: Probing the Fluorescent Media in the Vicinity of the Noise-Defined Threshold

A method of reference-free speckle spectroscopy based on the statistical analysis of intensity spatial fluctuations of the spectrally-selected multiple-scattered fluorescence radiation is examined in the case of the finite-band spectral selection of fluorescence light emitted by the laser-pumped random medium, and detection conditions far from the ideal case. Intensity fluctuations are recorded during point-to-point scanning of the surface of a random multiple-scattering medium, which is characterized by the dependences of the second- and third-order statistical moments of intensity on the wavelength of detected spectrally selected light. In turn, the statistical moments of intensity fluctuations are determined by the average propagation path of fluorescent radiation in the medium. This makes it possible to analyze the features of the light-medium interactions at a scale of the order of the transport mean free path of radiation propagation in the medium. Depending on the spectral selection conditions, the method is applicable for characterizing micro- or nano-structured fluorescent layers with thicknesses from tens of micrometers to several millimeters. In the examined case, the finite-band spectral selection results in the values of coherence length of the detected fluorescence radiation compared with the ensemble-averaged absolute value of the path-length difference between the stochastically interfering and spectrally selected partial contributions to the fluorescence field. In addition, non-ideal detection conditions (usage of a multimode optical fiber in the light-collecting unit) cause additional strong damping of the detected speckle intensity fluctuations. These factors lead to a remarkable suppression of spatial fluctuations of the fluorescence intensity in the course of spatially- and spectrally-resolved surface scanning of the laser-pumped probed random medium. Nevertheless, with appropriate procedures of the intrinsic noise reduction and data correction, the obtained spectral dependencies of the normalized third-order statistical moment of the band-limited fluorescence intensity clearly indicate the fluorescence propagation features in the probed multiple-scattering random media (such as a strong influence of the scattering strength and multiple self-absorption–re-emission events on the average propagation path of light in the medium).The possibilities of noise reduction and data correction in the case of applying the band-limited reference-free spectroscopic instrumentation with low spectral and spatial resolution are illustrated by the experimental results obtained using the Rhodamine-6G-doped and continuous wave (CW)-laser-pumped layers of the densely packed titania and silica particles.

Role of electronic kinetic energy and resultant gradient information in chemical reactivity

The role of resultant gradient-information concept, reflecting the kinetic energy of electrons, in shaping the molecular electronic structure and reactivity preferences of open reactants is examined. This quantum-information descriptor combines contributions due to both the modulus (probability) and phase (current) components of electronic wavefunctions. The importance of resultant entropy/information concepts for distinguishing the bonded (entangled) and nonbonded (disentangled) states of molecular fragments is emphasized and variational principle for the minimum of ensemble-average electronic energy is interpreted as a physically equivalent rule for the minimum of resultant gradient-information, and the information descriptors of charge-transfer (CT) phenomena are introduced. The in situ reactivity criteria, represented by the populational CT derivatives of the ensemble-average values of electronic energy or resultant information, are mutually related, giving rise to identical predictions of electron flows in the acid(A) — base(B), reactive systems. The virial theorem decomposition of electronic energy is used to reveal changes in the resultant information content due to the chemical bond formation, and to rationalize the Hammond postulate of reactivity theory. The complementarity principle of structural chemistry is confronted with the regional hard (soft) acid and bases (HSAB) rule by examining the polarizational and relaxational flows in such acceptor–donor reactive systems, responses to the external potential and CT displacements, respectively. The frontier-electron basis of the HSAB principle is reexamined and the intra- and inter-reactant communications in A—B systems are explored.

Average dark matter halo sparsity relations as consistency check of mass estimates in galaxy cluster samples

The dark matter halo sparsity provides a direct observational proxy of the halo mass profile, characterizing halos in terms of the ratio of masses within radii which enclose two different overdensities. Previous numerical simulation analyses have shown that at a given redshift the halo sparsity carries cosmological information encoded in the halo mass profile. Moreover, its ensemble-averaged value can be inferred from prior knowledge of the halo mass function at the overdensities of interest. Here, we present a detailed study of the ensemble average properties of the halo sparsity. In particular, using halo catalogues from high-resolution N-body simulations, we show that its ensemble average value can be estimated from the ratio of the averages of the inverse halo masses as well as the ratio of the averages of the halo masses at the overdensity of interests. This can be relevant for galaxy clusters data analyses. As an example, we have estimated the average sparsity properties of galaxy clusters from the LoCuSS and HIFLUGCS data sets, respectively. The results suggest that the expected consistency of the different average sparsity estimates can provide a test of the robustness of mass measurements in galaxy cluster samples.

Thermal Behaviour of Zr65Cu17.5Ni10Al7.5 Glassy Alloy

Estimating entropy of glass cannot be performed using the time-dependent and irreversible part of the heat capacity (Cp) which is measured in the glass-formation range. The difference of the estimate and the real change in entropy can be determined by calculating the change in the CpdT and CpdlnT integrals before and after isothermal annealing by using DSC. In this paper, we report this estimation difference for Zr65Cu17.5Ni10Al7.5 glassy alloy. The minimized annealing results in the CpdlnT integrals for the cooling and the heating paths approach the same value. We affirm that entropy is an ensemble-averaged value since the Clausius limits show that the estimation of the residual entropy is not affected significantly by irreversibility and its value can be estimated from the Cp data.

Local instantaneous heat transfer around a single elongated bubble in inclined pipes

The instantaneous convective heat transfer rate resulting from the passage of a single elongated bubble propagating in an inclined pipe with a constant translational velocity is examined experimentally for various pipe inclinations and liquid flow rates. Local instantaneous heat transfer rates in the upper and lower parts of the pipe were determined using wall temperature measurements by an IR camera. The ensemble-averaged values of the heat transfer rate are presented as a function of the distance from either the bubble tip or bottom. Optical sensors synchronized with the IR camera were used for this purpose. Possible mechanisms that govern the enhancement of the heat transfer rate during the passage of an elongated bubble are discussed.

Reproducing the Ensemble Average Polar Solvation Energy of a Protein from a Single Structure: Gaussian-Based Smooth Dielectric Function for Macromolecular Modeling.

Typically, the ensemble average polar component of solvation energy (ΔGpolarsolv) of a macromolecule is computed using molecular dynamics (MD) or Monte Carlo (MC) simulations to generate conformational ensemble and then single/rigid conformation solvation energy calculation is performed on each snapshot. The primary objective of this work is to demonstrate that Poisson-Boltzmann (PB)-based approach using a Gaussian-based smooth dielectric function for macromolecular modeling previously developed by us (Li et al. J. Chem. Theory Comput. 2013, 9 (4), 2126-2136) can reproduce that ensemble average (ΔGpolarsolv) of a protein from a single structure. We show that the Gaussian-based dielectric model reproduces the ensemble average ΔGpolarsolv(⟨ΔGpolarsolv⟩) from an energy-minimized structure of a protein regardless of the minimization environment (structure minimized in vacuo, implicit or explicit waters, or crystal structure); the best case, however, is when it is paired with an in vacuo-minimized structure. In other minimization environments (implicit or explicit waters or crystal structure), the traditional two-dielectric model can still be selected with which the model produces correct solvation energies. Our observations from this work reflect how the ability to appropriately mimic the motion of residues, especially the salt bridge residues, influences a dielectric model's ability to reproduce the ensemble average value of polar solvation free energy from a single in vacuo-minimized structure.

Laboratory study of temporal and spatial evolution of waves excited on water surface initially at rest by impulsive wind forcing

Evolution of waves excited by wind that varies in time is not yet understood sufficiently well. In the present study, waves generated from rest by an effectively impulsive wind forcing are studied in a small laboratory wind-wave tank. Multiple parameters characterizing evolution of the wave field in time as well as in space are presented. Measurements of the variation with time of the instantaneous surface elevation were performed simultaneously with determination of two components of the instantaneous surface slope at a number of fetches along the test section. For each wind forcing conditions, numerous independent realizations were recorded. Thus, sufficient data were collected for computation of statistically reliable ensemble-averaged values of parameters characterizing the evolving random wind-wave field as a function of time elapsed since the initiation of wind. In each realization, data acquisition started when the water surface was calm, and lasted until statistically steady random wave field conditions were attained. The analysis of the ensemble-averaged wind-wave characteristics indicated that distinct stages in the wind-waves evolution could be identified. These stages were compared with the predictions based on the viscous instability theory and on the random resonant wind-waves generation model.

Vibrational Probes: From Small Molecule Solvatochromism Theory and Experiments to Applications in Complex Systems.

The vibrational frequency of a chosen normal mode is one of the most accurately measurable spectroscopic properties of molecules in condensed phases. Accordingly, infrared absorption and Raman scattering spectroscopy have provided valuable information on both distributions and ensemble-average values of molecular vibrational frequencies, and these frequencies are now routinely used to investigate structure, conformation, and even absolute configuration of chemical and biological molecules of interest. Recent advancements in coherent time-domain nonlinear vibrational spectroscopy have allowed the study of heterogeneous distributions of local structures and thermally driven ultrafast fluctuations of vibrational frequencies. To fully utilize IR probe functional groups for quantitative bioassays, a variety of biological and chemical techniques have been developed to site-specifically introduce vibrational probe groups into proteins and nucleic acids. These IR-probe-labeled biomolecules and chemically reactive systems are subject to linear and nonlinear vibrational spectroscopic investigations and provide information on the local electric field, conformational changes, site-site protein contacts, and/or function-defining features of biomolecules. A rapidly expanding library of data from such experiments requires an interpretive method with atom-level chemical accuracy. However, despite prolonged efforts to develop an all-encompassing theory for describing vibrational solvatochromism and electrochromism as well as dynamic fluctuations of instantaneous vibrational frequencies, purely empirical and highly approximate theoretical models have often been used to interpret experimental results. They are, in many cases, based on the simple assumption that the vibrational frequency of an IR reporter is solely dictated by electric potential or field distribution around the vibrational chromophore. Such simplified description of vibrational solvatochromism generally referred to as vibrational Stark effect theory has been considered to be quite appealing and, even in some cases, e.g., carbonyl stretch modes in amide, ester, ketone, and carbonate compounds or proteins, it works quantitatively well, which makes it highly useful in determining the strength of local electric field around the IR chromophore. However, noting that the vibrational frequency shift results from changes of solute-solvent intermolecular interaction potential along its normal coordinate, Pauli exclusion repulsion, polarization, charge transfer, and dispersion interactions, in addition to the electrostatic interaction between distributed charges of both vibrational chromophore and solvent molecules, are to be properly included in the theoretical description of vibrational solvatochromism. Since the electrostatic and nonelectrostatic intermolecular interaction components have distinctively different distance and orientation dependences, they affect the solvatochromic vibrational properties in a completely different manner. Over the past few years, we have developed a systematic approach to simulating vibrational solvatochromic data based on the effective fragment potential approach, one of the most accurate and rigorous theories on intermolecular interactions. We have further elucidated the interplay of local electric field with the general vibrational solvatochromism of small IR probes in either solvents or complicated biological systems, with emphasis on contributions from non-Coulombic intermolecular interactions to vibrational frequency shifts and fluctuations. With its rigorous foundation and close relation to quantitative interpretation of experimental data, this and related theoretical approaches and experiments will be of use in studying and quantifying the structure and dynamics of biomolecules with unprecedented time and spatial resolution when combined with time-resolved vibrational spectroscopy and chemically sensitive vibrational imaging techniques.