Framework Of Statistical Mechanics Research Articles

The structure of musical harmony as an ordered phase of sound: A statistical mechanics approach to music theory.

Music, while allowing nearly unlimited creative expression, almost always conforms to a set of rigid rules at a fundamental level. The description and study of these rules, and the ordered structures that arise from them, is the basis of the field of music theory. Here, I present a theoretical formalism that aims to explain why basic ordered patterns emerge in music, using the same statistical mechanics framework that describes emergent order across phase transitions in physical systems. I first apply the mean field approximation to demonstrate that phase transitions occur in this model from disordered sound to discrete sets of pitches, including the 12-fold octave division used in Western music. Beyond the mean field model, I use numerical simulation to uncover emergent structures of musical harmony. These results provide a new lens through which to view the fundamental structures of music and to discover new musical ideas to explore.

Coarse-graining involving virtual sites: Centers of symmetry coarse-graining.

Coarse-grained (CG) models allow efficient molecular simulation by reducing the degrees of freedom in the system. To recapitulate important physical properties, including many-body correlations at the CG resolution, an appropriate mapping from the atomistic to CG level is needed. Symmetry exhibited by molecules, especially when aspherical, can be lost upon coarse-graining due to the use of spherically symmetric CG effective potentials. This mismatch can be efficiently amended by imposing symmetry using virtual CG sites. However, there has been no rigorous bottom-up approach for constructing a many-body potential of mean force that governs the distribution of virtual CG sites. Herein, we demonstrate a statistical mechanical framework that extends a mapping scheme of CG systems involving virtual sites to provide a thermodynamically consistent CG model in the spirit of the principle of maximum entropy. Utilizing the extended framework, this work defines a center of symmetry (COS) mapping and applies it to benzene and toluene systems such that the planar symmetry of the aromatic ring is preserved by constructing two virtual sites along a normal vector. Compared to typical center of mass (COM) CG models, COS CG models correctly recapitulate radial and higher order correlations, e.g., orientational and three-body correlations. Moreover, we find that COS CG interactions from bulk phases are transferable to mixture phases, whereas conventional COM models deviate between the two states. This result suggests a systematic approach to construct more transferable CG models by conserving molecular symmetry, and the new protocol is further expected to capture other many-body correlations by utilizing virtual sites.

The effect of thermal magnonic excitations on the electronic conductance of a magnetic nanowire

Abstract In this paper, we study the effect of thermal magnonic excitations on the electronic conductance of an anti-ferromagnetic nanowire which is coupled to two electrodes in the framework of equilibrium statistical mechanics. The electron-magnon scattering is assumed to be present only in the center part, not in the electrodes. For each magnonic mode of the chain, we calculate a Green’s function and the corresponding mode-dependent transmission coefficient via the linear response theory. Then, the total electronic transmission through the system is obtained by the summation of the mode-dependent ones. We examine the influence of magnonic waves on three different configurations for the center wire including uniform, alternative on-site (AB) and polyacetylene like (PA-like) chain. Two types of nonmagnetic and ferromagnetic structures are chosen for the left and right leads. The results show that the effect of magnonic excitations on the electronic conductance of the considered systems is important at high temperatures. Especially, the electron tunneling conductance is improved in the presence of magnonic excitations in the PA-like and AB nanowires in contrast to the uniform one. While for all configurations, the conductance decreases in the resonance region by increasing the magnonic effects. Finally, we discuss the spin polarization and we show that the effect of thermal magnonic excitations is more observable in AB with respect to PA-like and in PA-like with respect to the uniform configuration of the center wire.

Ensemble in phase space: Statistical formalism of quantum mechanics

We present an alternative formalism of quantum mechanics tailored to statistical ensemble in phase space. The purpose of our work is to show that it is possible to establish an alternative autonomous formalism of quantum mechanics in phase space using statistical methodology. The adopted perspective leads to obtaining within the framework of its theory the master quantum-mechanical equation without recourse to the other formalisms of quantum mechanics, and gives the idea of operators pertaining to dynamical quantities. The derivation of this equation starts with the ensemble in phase space. We have explained with the help of this equation the structure of quantum mechanics in phase space and the approximation to the Schrodinger equation. Furthermore, we have shown that this formalism provides reasonable results of quantization by dealing with some simple cases, which confirm the validity of this formalism. In particular, we have demonstrated that this formalism can easily give the relativistic wave equation without treating the problem of linearizing the Hamiltonian operator by making the most of the point that the master equation is a first-order partial differential equation with respect to time, position and momentum variables, and makes use of the phase velocity. The ultimate outcome this formalism produces is that primary and general matters of quantum mechanics can be studied reasonably within the framework of statistical mechanics.

Demonstration of protein cooperativity mediated by RNA structure using the human protein PUM2

Posttranslational gene regulation requires a complex network of RNA–protein interactions. Cooperativity, which tunes response sensitivities, originates from protein–protein interactions in many systems. For RNA-binding proteins, cooperativity can also be mediated through RNA structure. RNA structural cooperativity (RSC) arises when binding of one protein induces a redistribution of RNA conformational states that enhance access (positive cooperativity) or block access (negative cooperativity) to additional binding sites. As RSC does not require direct protein–protein interactions, it allows cooperativity to be tuned for individual RNAs, via alterations in sequence that alter structural stability. Given the potential importance of this mechanism of control and our desire to quantitatively dissect features that underlie physiological regulation, we developed a statistical mechanical framework for RSC and tested this model by performing equilibrium binding measurements of the human PUF family protein PUM2. Using 68 RNAs that contain two to five PUM2-binding sites and RNA structures of varying stabilities, we observed a range of structure-dependent cooperative behaviors. To test our ability to account for this cooperativity with known physical constants, we used PUM2 affinity and nearest-neighbor RNA secondary structure predictions. Our model gave qualitative agreement for our disparate set of 68 RNAs across two temperatures, but quantitative deviations arise from overestimation of RNA structural stability. Our results demonstrate cooperativity mediated by RNA structure and underscore the power of quantitative stepwise experimental evaluation of mechanisms and computational tools.

On the structure of a confined ideal gas: A statistical mechanical description with an external field

All fluids are somehow confined; even the ideal gas is by definition a confined fluid model. For all practical purposes, if the distance between the confining walls is reasonably large, the confinement effect is negligible. Nevertheless, whenever this distance is about a few nanometers, the confinement effect is unavoidable, and is manifested as an inhomogeneity in the fluid particles distribution. Here, a statistical mechanical framework from which the structure of a confined ideal gas can be directly calculated is derived. As a case study, the structure of an ideal gas confined by planar graphite walls is determined with the proposed theory and compared to Monte Carlo simulations. The gratifyingly perfect agreement between these two approaches shows the correctness of the proposed theory. The influences of pore size and temperature are analyzed. The theoretical results obtained here serve as a limit that is obeyed by any low density confined fluid.

К выводу симметричности матрицы кинетических коэффициентов Онсагера в рамках неэкстенсивной статистической механики Тсаллиса

К выводу симметричности матрицы кинетических коэффициентов Онсагера в рамках неэкстенсивной статистической механики Тсаллиса

Statistical mechanical modeling of a DNA nanobiostructure at the base-pair level

We have modeled a double-stranded DNA nanostructure within the framework of statistical mechanics and ensemble theory as composed of a large number of base pairs with rotational degrees of freedom around the bases to generate helical or bent configurations. Different binding energies associated with the two kinds of the base pairs have been found only via statistical considerations and as an implication of the tendency of the system to minimize its free energy irrespective of the nature or the number of bonds making the base pairs. The temperature-dependent alternative for the relation of information capacity has been also derived in the canonical formalism as a more realistic expression compared to its microcanonical counterpart with a possible importance in DNA-based, information-bearing, nano-scale devices. Results demonstrate the degeneracy associated with the rotational degrees of freedom as a potential factor for further increasing the information capacity of such a nanobiostructure.

The homeostatic ensemble for cells

Cells are quintessential examples of out-of-equilibrium systems, but they maintain a homeostatic state over a timescale of hours to days. As a consequence, the statistics of all observables is remarkably consistent. Here, we develop a statistical mechanics framework for living cells by including the homeostatic constraint that exists over the interphase period of the cell cycle. The consequence is the introduction of the concept of a homeostatic ensemble and an associated homeostatic temperature, along with a formalism for the (dynamic) homeostatic equilibrium that intervenes to allow living cells to evade thermodynamic decay. As a first application, the framework is shown to accurately predict the observed effect of the mechanical environment on the in vitro response of smooth muscle cells. This includes predictions that both the mean values and diversity/variability in the measured values of observables such as cell area, shape and tractions decrease with decreasing stiffness of the environment. Thus, we argue that the observed variabilities are inherent to the entropic nature of the homeostatic equilibrium of cells and not a result of in vitro experimental errors.

Statistical equilibrium in quantum gravity: Gibbs states in group field theory

Gibbs states are known to play a crucial role in the statistical description of a system with a large number of degrees of freedom. They are expected to be vital also in a quantum gravitational system with many underlying fundamental discrete degrees of freedom. However, due to the absence of well-defined concepts of time and energy in background independent settings, formulating statistical equilibrium in such cases is an open issue. This is even more so in a quantum gravity context that is not based on any of the usual spacetime structures, but on non-spatiotemporal degrees of freedom. In this paper, after having clarified general notions of statistical equilibrium, on which two different construction procedures for Gibbs states can be based, we focus on the group field theory (GFT) formalism for quantum gravity, whose technical features prove advantageous to the task. We use the operator formulation of GFT to define its statistical mechanical framework, based on which we construct three concrete examples of Gibbs states. The first is a Gibbs state with respect to a geometric volume operator, which is shown to support condensation to a low-spin phase. This state is not based on a pre-defined symmetry of the system and its construction is via Jaynes’ entropy maximisation principle. The second are Gibbs states encoding structural equilibrium with respect to internal translations on the GFT base manifold, and defined via the KMS condition. The third are Gibbs states encoding relational equilibrium with respect to a clock Hamiltonian, obtained by deparametrization with respect to coupled scalar matter fields.

A new approach to the generalization of Planck’s law of black-body radiation

In this study, Planck’s law of black-body radiation has been modified within the framework of nonextensive statistical mechanics. The average energy of radiation has been derived by introducing the nonextensive partition function in the statistical relation of internal energy. The spectral energy density and spectral radiance have also been computed. The derived expression has been compared with the earlier developed approximate schemes (i.e. asymptotic approach and factorization approach) and with the recently obtained exact result. We utilize the exact and approximate Stefan–Boltzmann laws in order to compare with the new approach introduced here.

Ambulance Service Resource Planning for Extreme Temperatures: Analysis of Ambulance 999 Calls during Episodes of Extreme Temperature in London, UK

The association between episodes of extreme temperature and ambulance 999 calls has not yet been properly quantified. In this study we propose a statistical physics-based method to estimate the true mean number of ambulance 999 calls during episodes of extreme temperatures. Simple arithmetic mean overestimates the true number of calls during such episodes. Specifically, we apply the physics-based framework of nonextensive statistical mechanics (NESM) for estimating the probability distribution of extreme events to model the positive daily variation of ambulance calls. In addition, we combine NESM with the partitioned multiobjective method (PMRM) to determine the true mean of the positive daily difference of calls during periods of extreme temperature. We show that the use of the standard mean overestimates the true mean number of ambulance calls during episodes of extreme temperature. It is important to correctly estimate the mean value of ambulance 999 calls during such episodes in order for the ambulance service to efficiently manage their resources.

Thermodynamic equilibrium with acceleration and the Unruh effect

We address the problem of thermodynamic equilibrium with constant acceleration along the velocity field lines in a quantum relativistic statistical mechanics framework. We show that for a free scalar quantum field, after vacuum subtraction, all mean values vanish when the local temperature T is as low as the Unruh temperature T_U = A/2\pi where A is the magnitude of the acceleration four-vector. We argue that the Unruh temperature is an absolute lower bound for the temperature of any accelerated fluid at global thermodynamic equilibrium. We discuss the conditions of this bound to be applicable in a local thermodynamic equilibrium situation.

Alkali Metal Ion Partitioning with Calix[4]arene-benzo-crown-6 Ionophore in Acidic Medium: Insights from Experiments, Statistical Mechanical Framework, and Molecular Dynamics Simulations.

The current work reports the experimental and predicted interfacial behavior of metal ion extraction from aqueous phase-diluent system using a newly synthesized calix-benzo-crown-6 (CBCBGA) ionophore. Conductor-like screening model for real solvents was used to predict the selectivity at infinite dilution for the metal ion complexes in both aqueous and diluent phases. The selectivity for Cs+-CBCBGA extraction was found to be higher than that of other metal ions, namely, K+, Na+, and Rb+. This was confirmed by the experimental distribution coefficients obtained in the diluents system at 3 M HNO3 along with 0.01 M CBCBGA/organic solvents. The high selectivity of Cs+-CBCBGA complex over other complexes (K+, Rb+, and Na+) in nitrobenzene was also confirmed and validated by the highest occupied molecular orbital-lowest unoccupied molecular orbital energy gap (i.e., 0.13114 > 0.12411 > 0.11719 > 0.11561 eV) and interaction energy (i.e., -68.25 > -57.11 > -55.52 > -52.37 kcal/mol). The interaction and free energies of the extraction were found to increase with the dielectric constant of the organic solvents, namely, nitrobenzene > o-nitrophenyl hexyl ether > 1-octanol > chloroform. Overall, a higher selectivity of Cs+ ion over that of other metal ions (K+, Na+, and Rb+) was obtained for the newly synthesized CBCBGA ionophore in a radioactive waste solution.

Derivation of the entropic formula for the statistical mechanics of space plasmas

Abstract. Kappa distributions describe velocities and energies of plasma populations in space plasmas. The statistical origin of these distributions is associated with the framework of nonextensive statistical mechanics. Indeed, the kappa distribution is derived by maximizing the q entropy of Tsallis, under the constraints of the canonical ensemble. However, the question remains as to what the physical origin of this entropic formulation is. This paper shows that the q entropy can be derived by adapting the additivity of energy and entropy.

Non-Gaussian Closed Form Solutions for Geometric Average Asian Options in the Framework of Non-Extensive Statistical Mechanics.

In this paper we consider pricing problems of the geometric average Asian options under a non-Gaussian model, in which the underlying stock price is driven by a process based on non-extensive statistical mechanics. The model can describe the peak and fat tail characteristics of returns. Thus, the description of underlying asset price and the pricing of options are more accurate. Moreover, using the martingale method, we obtain closed form solutions for geometric average Asian options. Furthermore, the numerical analysis shows that the model can avoid underestimating risks relative to the Black-Scholes model.

A Study of the Physical Properties of Li-Ion Battery Electrolytes Containing Esters

Adding esters as co-solvents to Li-ion battery electrolytes can improve low-temperature performance and rate capability of cells. This work uses viscosity and electrolytic conductivity measurements to evaluate electrolytes containing various ester co-solvents, and their suitability for use in high-rate applications is probed. Among the esters studied, methyl acetate (MA) outperforms other esters in its impact on the conductivity and viscosity of the electrolyte. Therefore, viscosity and conductivity were measured as a function of temperature and LiPF6 concentration for electrolytes ethylene carbonate (EC): linear carbonate: MA in the ratio 30:(70-x):x, where linear carbonate = {ethyl methyl carbonate (EMC), dimethyl carbonate (DMC)}, and x = {0, 10, 20, 30}. Adding MA leads to an increase in conductivity and decrease in viscosity over all conditions. Calculations of electrolyte properties from a model based on a statistical-mechanical framework, the Advanced Electrolyte Model (AEM), are compared to all measurements and excellent agreement is found. All electrolytes studied roughly agree with a Stokes’ Law model of conductivity. A Walden analysis shows that the ionicity of the electrolyte is not significantly impacted by either MA content or LiPF6 concentration. Li[Ni0.5Mn0.3Co0.2]O2/graphite cells containing MA were cycled at charging rates up to 2C and showed improved cycling performance.

Thermal inclusions: how one spin can destroy a many-body localized phase.

Many-body localized (MBL) systems lie outside the framework of statistical mechanics, as they fail to equilibrate under their own quantum dynamics. Even basic features of MBL systems, such as their stability to thermal inclusions and the nature of the dynamical transition to thermalizing behaviour, remain poorly understood. We study a simple central spin model to address these questions: a two-level system interacting with strength J with N≫1 localized bits subject to random fields. On increasing J, the system transitions from an MBL to a delocalized phase on the vanishing scale Jc(N)∼1/N, up to logarithmic corrections. In the transition region, the single-site eigenstate entanglement entropies exhibit bimodal distributions, so that localized bits are either 'on' (strongly entangled) or 'off' (weakly entangled) in eigenstates. The clusters of 'on' bits vary significantly between eigenstates of the same sample, which provides evidence for a heterogeneous discontinuous transition out of the localized phase in single-site observables. We obtain these results by perturbative mapping to bond percolation on the hypercube at small J and by numerical exact diagonalization of the full many-body system. Our results support the arguments that the MBL phase is unstable in systems with short-range interactions and quenched randomness in dimensions d that are high but finite.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

Symmetry-adapted order parameters and free energies for solids undergoing order-disorder phase transitions

Order-disorder phase transitions are common in a wide range of materials and are exploited in many technological applications. A key challenge in developing predictive mesoscale models for these materials lies in constructing rigorous first-principles based thermodynamic descriptions. In this study, the authors develop a general formalism to generate order parameters for any crystal structure and alloy ordering. Furthermore, they describe a thermodynamic and statistical mechanics framework to determine the free energy as a function of order parameters. The methods described here are broadly applicable to any multicomponent crystalline solid and provide the first step in generating truly $a\phantom{\rule{0}{0ex}}b\phantom{\rule{0.333em}{0ex}}i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ multiscale models.

Addressing the statistical mechanics of planet orbits in the solar system

The chaotic nature of planet dynamics in the solar system suggests the relevance of a statistical approach to planetary orbits. In such a statistical description, the time-dependent position and velocity of the planets are replaced by the probability density function (PDF) of their orbital elements. It is quite natural to set up this kind of approach in the framework of statistical mechanics. In the present paper I focus on the collisionless excitation of eccentricities and inclinations by gravitational interactions in a planetary system, the prototype of such a dynamics being the future planet trajectories in the solar system. I thus address the statistical mechanics of the planetary orbits in the solar system and try to reproduce the PDFs numerically constructed by Laskar (2008). I show that the microcanonical ensemble of the Laplace-Lagrange theory accurately reproduce the statistics of the giant planet orbits. To model the inner planets I then investigate the ansatz of equiprobability in the phase space constrained by the secular integrals of motion. The eccentricity and inclination PDFs of Earth and Venus are reproduced with no free parameters. Within the limitations of a stationary model, the predictions also show a reasonable agreement with Mars PDFs and that of Mercury inclination. The eccentricity of Mercury demands in contrast a deeper analysis. I finally revisit Laskar's random walk approach to the time dependence of the inner planet PDFs. Such a statistical theory could be combined with direct numerical simulations of planet trajectories in the context of planet formation, which is likely to be a chaotic process.