Journal articles: 'Nonequilibrium partition function'

1

Wang, Baigeng, Jian Wang, and Hong Guo. "Current Partition: A Nonequilibrium Green's Function Approach." Physical Review Letters 82, no. 2 (January 11, 1999): 398–401. http://dx.doi.org/10.1103/physrevlett.82.398.

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2

Al-Ghoul, Mazen, and Byung Chan Eu. "Nonequilibrium partition function in the presence of heat flow." Journal of Chemical Physics 115, no. 18 (November 8, 2001): 8481–88. http://dx.doi.org/10.1063/1.1410381.

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3

Eu, Byung Chan. "Note on the nonequilibrium partition function and generalized potentials." Journal of Chemical Physics 105, no. 13 (October 1996): 5525–28. http://dx.doi.org/10.1063/1.472393.

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4

LEV, B. I. "NONEQUILIBRIUM SELF-GRAVITATING SYSTEM." International Journal of Modern Physics B 25, no. 16 (June 30, 2011): 2237–49. http://dx.doi.org/10.1142/s0217979211100771.

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A new approach to the statistical description of a self-gravitating system has been proposed. The approach employs a nonequilibrium statistical operator that involves into consideration inhomogeneous distributions of particles and temperature. The states with dominant contributions to the partition function are found in terms of the saddle-point method that yields all the thermodynamic relations for a self-gravitating system. The approach makes it possible to describe new peculiar features in the behavior of the gravitating system under various external conditions; it may be applied to describe the formation of stars and galaxies.

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5

Skorik, Sergei. "Exact nonequilibrium current from the partition function for impurity-transport problems." Physical Review B 57, no. 20 (May 15, 1998): 12772–80. http://dx.doi.org/10.1103/physrevb.57.12772.

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6

Babou, Y., Ph Rivière, M. Y. Perrin, and A. Soufiani. "High-Temperature and Nonequilibrium Partition Function and Thermodynamic Data of Diatomic Molecules." International Journal of Thermophysics 30, no. 2 (November 13, 2007): 416–38. http://dx.doi.org/10.1007/s10765-007-0288-6.

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7

P Morriss, Gary, and Lamberto Rondoni. "Chaos and Its Impact on the Foundations of Statistical Mechanics." Australian Journal of Physics 49, no. 1 (1996): 51. http://dx.doi.org/10.1071/ph960051.

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In this work we present a brief derivation of the periodic orbit expansion for simple dynamical systems, and then we apply it to the study of a classical statistical mechanical model, the Lorentz gas, both at equilibrium and in a nonequilibrium steady state. The results are compared with those obtained through standard molecular dynamics simulations, and they are found to be in good agreement. The form of the average using the periodic orbit expansion suggests the definition of a new dynamical partition function, which we test numerically. An analytic formula is obtained for the Lyapunov numbers of periodic orbits for the nonequilibrium Lorentz gas. Using this formula and other numerical techniques we study the nonequilibrium Lorentz gas as a dynamical system and obtain an estimate of the upper bound on the external field for which the system remains ergodic.

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8

BENA, IOANA, MICHEL DROZ, and ADAM LIPOWSKI. "STATISTICAL MECHANICS OF EQUILIBRIUM AND NONEQUILIBRIUM PHASE TRANSITIONS: THE YANG–LEE FORMALISM." International Journal of Modern Physics B 19, no. 29 (November 20, 2005): 4269–329. http://dx.doi.org/10.1142/s0217979205032759.

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Showing that the location of the zeros of the partition function can be used to study phase transitions, Yang and Lee initiated an ambitious and very fruitful approach. We give an overview of the results obtained using this approach. After an elementary introduction to the Yang–Lee formalism, we summarize results concerning equilibrium phase transitions. We also describe recent attempts and breakthroughs in extending this theory to nonequilibrium phase transitions.

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KHOTIMAH, SITI NURUL, IDAM ARIF, and THE HOUW LIONG. "LATTICE-GAS AUTOMATA FOR THE PROBLEM OF KINETIC THEORY OF GAS DURING FREE EXPANSION." International Journal of Modern Physics C 13, no. 08 (October 2002): 1033–45. http://dx.doi.org/10.1142/s0129183102003772.

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The lattice-gas method has been applied to solve the problem of kinetic theory of gas in the Gay–Lussac–Joule experiment. Numerical experiments for a two-dimensional gas were carried out to determine the number of molecules in one vessel (Nr), the ratio between the mean square values of the components of molecule velocity [Formula: see text], and the change in internal energy (ΔU) as a function of time during free expansion. These experiments were repeated for different sizes of an aperture in the partition between the two vessels. After puncturing the partition, the curve for the particle number in one vessel shows a damped oscillation for about half of the total number. The oscillations do not vanish after a sampling over different initial configurations. The system is in nonequilibrium due to the pressure equilibration, and here the flow is actually compressible. The equilibration time (in time steps) decreases with decreased size of aperture in the partition. For very small apertures (equal or less than [Formula: see text] lattice units), the number of molecules in one vessel changes with time in a smooth way until it reaches half of the total number; their curves obey the analytical solution for quasi-static processes. The calculations on [Formula: see text] and ΔU also support the results that the equilibration time decreases with decreased size of aperture in the partition.

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10

BI, Lev, and Zagorodny AG. "Thermodynamic-induced geometry of self-gravitating systems." Annals of Mathematics and Physics 5, no. 2 (September 16, 2022): 130–34. http://dx.doi.org/10.17352/amp.000052.

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A new approach based on the nonequilibrium statistical operator is presented that makes it possible to take into account the inhomogeneous particle distribution and provides obtaining all thermodynamic relations of self-gravitating systems. The equations corresponding to the extremum of the partition function completely reproduce the well-known equations of the general theory of relativity. Guided by the principle of Mach's "economing of thinking" quantitatively and qualitatively, is shown that the classical statistical description and the associated thermodynamic relations reproduce Einstein's gravitational equation. The article answers the question of how is it possible to substantiate the general relativistic equations in terms of the statistical methods for the description of the behavior of the system in the classical case.

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11

Lim, Hyuntae, and YounJoon Jung. "Reaction-path statistical mechanics of enzymatic kinetics." Journal of Chemical Physics 156, no. 13 (April 7, 2022): 134108. http://dx.doi.org/10.1063/5.0075831.

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We introduce a reaction-path statistical mechanics formalism based on the principle of large deviations to quantify the kinetics of single-molecule enzymatic reaction processes under the Michaelis–Menten mechanism, which exemplifies an out-of-equilibrium process in the living system. Our theoretical approach begins with the principle of equal a priori probabilities and defines the reaction path entropy to construct a new nonequilibrium ensemble as a collection of possible chemical reaction paths. As a result, we evaluate a variety of path-based partition functions and free energies by using the formalism of statistical mechanics. They allow us to calculate the timescales of a given enzymatic reaction, even in the absence of an explicit boundary condition that is necessary for the equilibrium ensemble. We also consider the large deviation theory under a closed-boundary condition of the fixed observation time to quantify the enzyme–substrate unbinding rates. The result demonstrates the presence of a phase-separation-like, bimodal behavior in unbinding events at a finite timescale, and the behavior vanishes as its rate function converges to a single phase in the long-time limit.

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12

Kawazura, Yohei, Michael Barnes, and Alexander A. Schekochihin. "Thermal disequilibration of ions and electrons by collisionless plasma turbulence." Proceedings of the National Academy of Sciences 116, no. 3 (December 31, 2018): 771–76. http://dx.doi.org/10.1073/pnas.1812491116.

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Does overall thermal equilibrium exist between ions and electrons in a weakly collisional, magnetized, turbulent plasma? And, if not, how is thermal energy partitioned between ions and electrons? This is a fundamental question in plasma physics, the answer to which is also crucial for predicting the properties of far-distant astronomical objects such as accretion disks around black holes. In the context of disks, this question was posed nearly two decades ago and has since generated a sizeable literature. Here we provide the answer for the case in which energy is injected into the plasma via Alfvénic turbulence: Collisionless turbulent heating typically acts to disequilibrate the ion and electron temperatures. Numerical simulations using a hybrid fluid-gyrokinetic model indicate that the ion–electron heating-rate ratio is an increasing function of the thermal-to-magnetic energy ratio, βi: It ranges from ∼0.05 at βi=0.1 to at least 30 for βi≳10. This energy partition is approximately insensitive to the ion-to-electron temperature ratio Ti/Te. Thus, in the absence of other equilibrating mechanisms, a collisionless plasma system heated via Alfvénic turbulence will tend toward a nonequilibrium state in which one of the species is significantly hotter than the other, i.e., hotter ions at high βi and hotter electrons at low βi. Spectra of electromagnetic fields and the ion distribution function in 5D phase space exhibit an interesting new magnetically dominated regime at high βi and a tendency for the ion heating to be mediated by nonlinear phase mixing (“entropy cascade”) when βi≲1 and by linear phase mixing (Landau damping) when βi≫1.

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13

Li, Y. F., W. L. Ma, and M. Yang. "Prediction of gas/particle partitioning of polybrominated diphenyl ethers (PBDEs) in global air: a theoretical study." Atmospheric Chemistry and Physics Discussions 14, no. 16 (September 10, 2014): 23415–51. http://dx.doi.org/10.5194/acpd-14-23415-2014.

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Abstract. Gas/particle (G / P) partitioning for most semivolatile organic compounds (SVOCs) is an important process that primarily governs their atmospheric fate, long-range atmospheric transport potential, and their routs to enter human body. All previous studies on this issue have been hypothetically derived from equilibrium conditions, the results of which do not predict results from monitoring studies well in most cases. In this study, a steady-state model instead of an equilibrium-state model for the investigation of the G / P partitioning behavior for polybrominated diphenyl ethers (PBDEs) was established, and an equation for calculating the partition coefficients under steady state (KPS) for PBDE congeners (log KPS = log KPE + logα) was developed, in which an equilibrium term (log KPE = log KOA + logfOM −11.91, where fOM is organic matter content of the particles) and a nonequilibrium term (logα, mainly caused by dry and wet depositions of particles), both being functions of log KOA (octanol-air partition coefficient), are included, and the equilibrium is a special case of steady state when the nonequilibrium term equals to zero. A criterion to classify the equilibrium and nonequilibrium status for PBDEs was also established using two threshold values of log KOA, log KOA1 and log KOA2, which divide the range of log KOA into 3 domains: equilibrium, nonequilibrium, and maximum partition domains; and accordingly, two threshold values of temperature t, tTH1 when log KOA = log KOA1 and tTH2 when log KOA = log KOA2, were identified, which divide the range of temperature also into the same 3 domains for each BDE congener. We predicted the existence of the maximum partition domain (the values of log KPS reach a maximum constant of −1.53) that every PBDE congener can reach when log KOA ≥ log KOA2, or t ≤ tTH2. The novel equation developed in this study was applied to predict the G / P partition coefficients of PBDEs for the published monitoring data worldwide, including Asia, Europe, North America, and the Arctic, and the results matched well with all the monitoring data, except those obtained at e-waste sites due to the unpredictable PBDE emissions at these sites. This study provided evidence that, the new developed steady-state-based equation is superior to the equilibrium-state-based equation that has been used in describing the G / P partitioning behavior in decades. We suggest that, the investigation on G / P partitioning behavior for PBDEs should be based on steady state, not equilibrium state, and equilibrium is just a special case of steady state when nonequilibrium factors can be ignored. We also believe that our new equation provides a useful tool for environmental scientists in both monitoring and modeling research on G / P partitioning for PBDEs and can be extended to predict G / P partitioning behavior for other SVOCs as well.

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14

Yang, Xingbo, Matthias Heinemann, Jonathon Howard, Greg Huber, Srividya Iyer-Biswas, Guillaume Le Treut, Michael Lynch, et al. "Physical bioenergetics: Energy fluxes, budgets, and constraints in cells." Proceedings of the National Academy of Sciences 118, no. 26 (June 17, 2021): e2026786118. http://dx.doi.org/10.1073/pnas.2026786118.

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Cells are the basic units of all living matter which harness the flow of energy to drive the processes of life. While the biochemical networks involved in energy transduction are well-characterized, the energetic costs and constraints for specific cellular processes remain largely unknown. In particular, what are the energy budgets of cells? What are the constraints and limits energy flows impose on cellular processes? Do cells operate near these limits, and if so how do energetic constraints impact cellular functions? Physics has provided many tools to study nonequilibrium systems and to define physical limits, but applying these tools to cell biology remains a challenge. Physical bioenergetics, which resides at the interface of nonequilibrium physics, energy metabolism, and cell biology, seeks to understand how much energy cells are using, how they partition this energy between different cellular processes, and the associated energetic constraints. Here we review recent advances and discuss open questions and challenges in physical bioenergetics.

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15

Beatty, K. M., and K. A. Jackson. "Orientation and Velocity Dependence of the Nonequilibrium Partition Coefficient." MRS Proceedings 398 (1995). http://dx.doi.org/10.1557/proc-398-113.

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ABSTRACTMonte Carlo simulations based on a Spin-1 Ising Model for binary alloys have been used to investigate the non-equilibrium partition coefficient (kneq ) as a function of solid-liquid interface velocity and orientation. In simulations of Si with a second component kneq is greater in the [111] direction than the [100] direction in agreement with experimental results reported by Aziz et al. The simulated partition coefficient scales with the square of the step velocity divided by the diffusion coefficient of the secondary component in the liquid.

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16

Hoglund, David E., and Michael J. Aziz. "Interface Stability During Rapid Directional Solidification." MRS Proceedings 205 (1990). http://dx.doi.org/10.1557/proc-205-325.

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AbstractAt the solidification velocities observed during pulsed laser annealing, the planar interface between solid and liquid is stabilized by capillarity and nonequilibrium effects such as solute trapping. We used Rutherford backscattering and electron microscopy to determine the nonequilibrium partition coefficient and critical concentration for breakdown of the planar interface as a function of interface velocity for Sn-implanted silicon. This allows us to test the applicability of the Mullins- Sekerka stability theory to interfaces not in local equilibrium and to test the Coriell-Sekerka and other theories for oscillatory instabilities.

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17

Ayyer, Arvind, and Volker Strehl. "The spectrum of an asymmetric annihilation process." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AN,..., Proceedings (January 1, 2010). http://dx.doi.org/10.46298/dmtcs.2884.

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International audience In recent work on nonequilibrium statistical physics, a certain Markovian exclusion model called an asymmetric annihilation process was studied by Ayyer and Mallick. In it they gave a precise conjecture for the eigenvalues (along with the multiplicities) of the transition matrix. They further conjectured that to each eigenvalue, there corresponds only one eigenvector. We prove the first of these conjectures by generalizing the original Markov matrix by introducing extra parameters, explicitly calculating its eigenvalues, and showing that the new matrix reduces to the original one by a suitable specialization. In addition, we outline a derivation of the partition function in the generalized model, which also reduces to the one obtained by Ayyer and Mallick in the original model. Dans un travail récent sur la physique statistique hors équilibre, un certain modèle d'exclusion Markovien appelé "processus d'annihilation asymétrique'' a été étudié par Ayyer et Mallick. Dans ce document, ils ont donné une conjecture précise pour les valeurs propres (avec les multiplicités) de la matrice stochastique. Ils ont en outre supposé que, pour chaque valeur propre, correspond un seul vecteur propre. Nous prouvons la première de ces conjectures en généralisant la matrice originale de Markov par l'introduction de paramètres supplémentaires, calculant explicitement ses valeurs propres, et en montrant que la nouvelle matrice se réduit à l'originale par une spécialisation appropriée. En outre, nous présentons un calcul de la fonction de partition dans le modèle généralisé, ce qui réduit également à celle obtenue par Ayyer et Mallick dans le modèle original.

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18

Civrais, Clément H. B., Craig White, and René Steijl. "Vibrational Modeling with an Anharmonic Oscillator Model in Direct Simulation Monte Carlo." Journal of Thermophysics and Heat Transfer, December 23, 2022, 1–15. http://dx.doi.org/10.2514/1.t6547.

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Vehicles undergoing hypersonic speed experience extreme aerothermodynamic conditions. Real gas effects cannot be neglected, and thus internal degrees of freedom of molecules being partially/fully excited must be carefully predicted in order to accurately capture the physics of the flowfield. Within direct simulation Monte Carlo solvers, a harmonic oscillator (HO) model, where the quantum levels are evenly spaced, is typically used for vibrational energy. A more realistic model is an anharmonic oscillator (aHO), in which the energy between quantum levels is not evenly spaced. In this work, the Morse-aHO model is compared against HO. The Morse-aHO model is implemented in the dsmcFoam+ solver, and the numerical results are in excellent agreement with analytical and potential energy surface solutions for the partition function, mean vibrational energy, and degrees of freedom. A method for measuring the vibrational temperature of the gas when using the anharmonic model in a direct simulation Monte Carlo solver is presented, which is essential for returning macroscopic fields. For important thermophysical properties of molecular oxygen, such as the specific heat capacity, it is shown that the aHO and HO models begin to diverge at temperatures above 1000 K, making the use of HO questionable for all but low-enthalpy flows. For the same gas, including the electronic energy mode significantly improves the accuracy of the specific heat prediction, compared to experimental data, for temperatures above 2000 K. For relaxation from a state of thermal nonequilibrium, it is shown that the aHO model results in a slightly lower equilibrium temperature. When applied to hypersonic flow over a cylinder, the aHO model results in a smaller shock standoff distance and lower peak temperatures.

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19

Dubuet, U., E. Pannier, and C. O. Laux. "Uncertainties in Multi-Temperature Nonequilibrium Partition Functions and Application to CO2." Journal of Quantitative Spectroscopy and Radiative Transfer, July 2022, 108314. http://dx.doi.org/10.1016/j.jqsrt.2022.108314.

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Journal articles on the topic 'Nonequilibrium partition function'

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