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Journal articles on the topic 'Nonequilibrim steady statte'

Author: Grafiati

Published: 20 April 2024

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1

Humenyuk, Y. A. "Thermodynamic Quantities of a Low-Density Gas in the Weakly Nonequilibrium Heat-Conduction Steady State." Ukrainian Journal of Physics 61, no. 5 (May 2016): 400–412. http://dx.doi.org/10.15407/ujpe61.05.0400.

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2

Baranyai, András. "Temperature of nonequilibrium steady-state systems." Physical Review E 62, no. 5 (November 1, 2000): 5989–97. http://dx.doi.org/10.1103/physreve.62.5989.

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3

Hayakawa, Hisao, and Atsushi Kawarada. "Nonequilibrium Steady State in Vibrating Granular Gases." Progress of Theoretical Physics Supplement 161 (2006): 195–98. http://dx.doi.org/10.1143/ptps.161.195.

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4

Hernández-Machado, A., and David Jasnow. "Stability of a nonequilibrium steady-state interface." Physical Review A 37, no. 2 (January 1, 1988): 656–59. http://dx.doi.org/10.1103/physreva.37.656.

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5

Ohta, Takao, and Takahiro Ohkuma. "Fluctuations and Response in Nonequilibrium Steady State." Journal of the Physical Society of Japan 77, no. 7 (July 15, 2008): 074004. http://dx.doi.org/10.1143/jpsj.77.074004.

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6

SEWELL, GEOFFREY L. "QUANTUM MACROSTATISTICAL THEORY OF NONEQUILIBRIUM STEADY STATES." Reviews in Mathematical Physics 17, no. 09 (October 2005): 977–1020. http://dx.doi.org/10.1142/s0129055x05002492.

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We provide a general macrostatistical formulation of nonequilibrium steady states of reservoir driven quantum systems. This formulation is centered on the large scale properties of the locally conserved hydrodynamical observables, and our basic physical assumptions comprise (a) a chaoticity hypothesis for the nonconserved currents carried by these observables, (b) an extension of Onsager's regression hypothesis to fluctuations about nonequilibrium states, and (c) a certain mesoscopic local equilibrium hypothesis. On this basis, we obtain a picture wherein the fluctuations of the hydrodynamical variables about a nonequilibrium steady state execute a Gaussian Markov process of a generalized Onsager–Machlup type, which is completely determined by the position dependent transport coefficients and the equilibrium entropy function of the system. This picture reveals that the transport coefficients satisfy a generalized form of the Onsager reciprocity relations in the nonequilibrium situation and that the spatial correlations of the hydrodynamical observables are generically of long range. This last result constitutes a model-independent quantum mechanical generalization of that obtained for special classical stochastic systems and marks a striking difference between the steady nonequilibrium and equilibrium states, since it is only at critical points that the latter carry long range correlations.

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7

Hershfield, Selman. "Reformulation of steady state nonequilibrium quantum statistical mechanics." Physical Review Letters 70, no. 14 (April 5, 1993): 2134–37. http://dx.doi.org/10.1103/physrevlett.70.2134.

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8

Dubkov, Alexander A., Pavel N. Makhov, and Bernardo Spagnolo. "Nonequilibrium steady-state distributions in randomly switching potentials." Physica A: Statistical Mechanics and its Applications 325, no. 1-2 (July 2003): 26–32. http://dx.doi.org/10.1016/s0378-4371(03)00179-1.

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9

Heide, Carsten, and Nikolai F. Schwabe. "Ensemble properties in quantum steady-state nonequilibrium theories." Physical Review B 57, no. 19 (May 15, 1998): 11862–65. http://dx.doi.org/10.1103/physrevb.57.11862.

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10

Hołyst, Robert, Karol Makuch, Konrad Giżyński, Anna Maciołek, and Paweł J. Żuk. "Fundamental Relation for Gas of Interacting Particles in a Heat Flow." Entropy 25, no. 9 (September 4, 2023): 1295. http://dx.doi.org/10.3390/e25091295.

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There is a long-standing question of whether it is possible to extend the formalism of equilibrium thermodynamics to the case of nonequilibrium systems in steady-states. We have made such an extension for an ideal gas in a heat flow. Here, we investigated whether such a description exists for the system with interactions: the van der Waals gas in a heat flow. We introduced a steady-state fundamental relation and the parameters of state, each associated with a single way of changing energy. The first law of nonequilibrium thermodynamics follows from these parameters. The internal energy U for the nonequilibrium states has the same form as in equilibrium thermodynamics. For the van der Waals gas, U(S*,V,N,a*,b*) is a function of only five parameters of state (irrespective of the number of parameters characterizing the boundary conditions): the effective entropy S*, volume V, number of particles N, and rescaled van der Waals parameters a*, b*. The state parameters, a*, b*, together with S*, determine the net heat exchange with the environment. The net heat differential does not have an integrating factor. As in equilibrium thermodynamics, the steady-state fundamental equation also leads to the thermodynamic Maxwell relations for measurable steady-state properties.

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11

Sandev, Trifce, Viktor Domazetoski, Ljupco Kocarev, Ralf Metzler, and Aleksei Chechkin. "Heterogeneous diffusion with stochastic resetting." Journal of Physics A: Mathematical and Theoretical 55, no. 7 (January 28, 2022): 074003. http://dx.doi.org/10.1088/1751-8121/ac491c.

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Abstract We study a heterogeneous diffusion process (HDP) with position-dependent diffusion coefficient and Poissonian stochastic resetting. We find exact results for the mean squared displacement and the probability density function. The nonequilibrium steady state reached in the long time limit is studied. We also analyse the transition to the non-equilibrium steady state by finding the large deviation function. We found that similarly to the case of the normal diffusion process where the diffusion length grows like t 1/2 while the length scale ξ(t) of the inner core region of the nonequilibrium steady state grows linearly with time t, in the HDP with diffusion length increasing like t p/2 the length scale ξ(t) grows like t p . The obtained results are verified by numerical solutions of the corresponding Langevin equation.

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12

Passlack, M., M. Hong, E. F. Schubert, G. J. Zydzik, J. P. Mannaerts, W. S. Hobson, and T. D. Harris. "Advancing metal–oxide–semiconductor theory: Steady-state nonequilibrium conditions." Journal of Applied Physics 81, no. 11 (June 1997): 7647–61. http://dx.doi.org/10.1063/1.365343.

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13

Gildenburg, V. B., I. A. Pavlichenko, and D. A. Smirnova. "Nonequilibrium steady-state discharge in the focused wave beam." Physics of Plasmas 25, no. 8 (August 2018): 084506. http://dx.doi.org/10.1063/1.5047785.

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14

Král, Petr. "Nonequilibrium linked cluster expansion for steady-state quantum transport." Physical Review B 56, no. 12 (September 15, 1997): 7293–303. http://dx.doi.org/10.1103/physrevb.56.7293.

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15

Taniguchi, Tooru, and E. G. D. Cohen. "Nonequilibrium Steady State Thermodynamics and Fluctuations for Stochastic Systems." Journal of Statistical Physics 130, no. 4 (December 15, 2007): 633–67. http://dx.doi.org/10.1007/s10955-007-9471-1.

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16

BOSE, INDRANI, and INDRANATH CHAUDHURI. "PERCOLATION-LIKE PHASE TRANSITION IN A NONEQUILIBRIUM STEADY STATE." International Journal of Modern Physics C 12, no. 02 (February 2001): 247–56. http://dx.doi.org/10.1142/s0129183101001651.

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We study the Gierer–Meinhardt model of reaction-diffusion on a site-disordered square lattice. Let p be the site occupation probability of the square lattice. For p greater than a critical value pc, the steady state consists of stripe-like patterns with long-range connectivity. For p < pc, the connectivity is lost. The value of pc is found to be much greater than that of the site percolation threshold for the square lattice. In the vicinity of pc, the cluster-related quantities exhibit power-law scaling behavior. The method of finite-size scaling is used to determine the values of the fractal dimension df, the ratio, γ/ν, of the average cluster size exponent γ and the correlation length exponent ν. The values appear to indicate that the disordered GM model belongs to the universality class of ordinary percolation.

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17

Blumenfeld, Raphael. "Nonequilibrium Brittle Fracture Propagation: Steady State, Oscillations, and Intermittency." Physical Review Letters 76, no. 20 (May 13, 1996): 3703–6. http://dx.doi.org/10.1103/physrevlett.76.3703.

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18

Gaudesius, Marius, Yong-Chang Zhang, Thomas Pohl, Guillaume Labeyrie, and Robin Kaiser. "Nonequilibrium Steady State in a Large Magneto-Optical Trap." Atoms 10, no. 4 (December 15, 2022): 153. http://dx.doi.org/10.3390/atoms10040153.

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Considering light-mediated long-range interactions between cold atoms in a magneto-optical trap (MOT), we present numerical evidence of a nonequilibrium steady state (NESS) for sufficiently large number of atoms (>108). This state manifests itself as the appearance of an anisotropic distribution of velocity when a MOT approaches the threshold beyond which self-oscillating instabilities occur. Our three-dimensional (3D) spatiotemporal model with nonlocal spatial dependencies stemming from the interatomic interactions has recently been compared successfully to predict different instability thresholds and regimes in experiments with rubidium atoms. The behavior of the NESS is studied as a function of the main MOT parameters, including its spatiotemporal characteristics.

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19

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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20

Mayer, Daniel, and Artur Widera. "Thermalization and Nonequilibrium Steady States in a Few-Atom System." Zeitschrift für Naturforschung A 75, no. 5 (May 26, 2020): 413–20. http://dx.doi.org/10.1515/zna-2020-0005.

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AbstractWe investigate nonequilibrium steady states in an isolated system of few ultracold cesium atoms (Cs). Numerically and experimentally, we study the dynamics and fluctuations of the extracted position distributions and find the formation of nonthermal steady states for absent interactions. Atomic collisions in the s-wave regime, however, ensue thermalization of the few-particle system. We present numerical simulations of the microscopic equations of motion with a simple representation of the s-wave scattering events. Based on these simulations, a parameter range is identified, where the interaction between few atoms is sufficiently strong to thermalize the nonequilibrium steady state on experimentally accessible time scales, which can be traced by monitoring the atomic position distribution. Furthermore, the total energy distribution, which is also accessible experimentally, is found to be a powerful tool to observe the emergence of a thermal state. Our work provides a pathway for future experiments investigating the effect interactions in few-particle systems and underlines the role of fluctuations in investigating few-particle systems.

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21

Noh, Jae Dong, and Joongul Lee. "On the steady-state probability distribution of nonequilibrium stochastic systems." Journal of the Korean Physical Society 66, no. 4 (February 2015): 544–52. http://dx.doi.org/10.3938/jkps.66.544.

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22

Janković, Veljko, and Tomáš Mančal. "Nonequilibrium steady-state picture of incoherent light-induced excitation harvesting." Journal of Chemical Physics 153, no. 24 (December 28, 2020): 244110. http://dx.doi.org/10.1063/5.0029918.

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23

Baranyai, András, and Peter T. Cummings. "Towards a computational chemical potential for nonequilibrium steady-state systems." Physical Review E 60, no. 5 (November 1, 1999): 5522–27. http://dx.doi.org/10.1103/physreve.60.5522.

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24

Trepagnier, E. H., C. Jarzynski, F. Ritort, G. E. Crooks, C. J. Bustamante, and J. Liphardt. "Experimental test of Hatano and Sasa's nonequilibrium steady-state equality." Proceedings of the National Academy of Sciences 101, no. 42 (October 6, 2004): 15038–41. http://dx.doi.org/10.1073/pnas.0406405101.

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25

Freericks, J. K. "Impurity problems for steady-state nonequilibrium dynamical mean-field theory." Physica E: Low-dimensional Systems and Nanostructures 42, no. 3 (January 2010): 520–24. http://dx.doi.org/10.1016/j.physe.2009.06.036.

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26

Speck, T., and U. Seifert. "Restoring a fluctuation-dissipation theorem in a nonequilibrium steady state." Europhysics Letters (EPL) 74, no. 3 (May 2006): 391–96. http://dx.doi.org/10.1209/epl/i2005-10549-4.

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27

Kita, Takafumi. "On the Density Matrix of Nonequilibrium Steady-State Statistical Mechanics." Journal of the Physical Society of Japan 71, no. 8 (August 2002): 1795–97. http://dx.doi.org/10.1143/jpsj.71.1795.

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28

Prudnikov, O. N., A. V. Taichenachev, and V. I. Yudin. "Essentially nonequilibrium steady state of atoms in an optical field." JETP Letters 102, no. 9 (November 2015): 576–80. http://dx.doi.org/10.1134/s0021364015210092.

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29

Sheehan, D. P., J. Glick, T. Duncan, J. A. Langton, M. Gagliardi, and R. Tobe. "Phase Space Analysis of a Gravitationally-Induced, Steady-State Nonequilibrium." Physica Scripta 65, no. 5 (January 1, 2002): 430–37. http://dx.doi.org/10.1238/physica.regular.065a00430.

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30

Subotnik, Joseph E., Thorsten Hansen, Mark A. Ratner, and Abraham Nitzan. "Nonequilibrium steady state transport via the reduced density matrix operator." Journal of Chemical Physics 130, no. 14 (April 14, 2009): 144105. http://dx.doi.org/10.1063/1.3109898.

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31

Grigin, A. P. "Nonequilibrium fluctuations of the rates of steady-state chemical reactions." Technical Physics Letters 23, no. 1 (January 1997): 16–17. http://dx.doi.org/10.1134/1.1261881.

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32

SAJOSCH, H. J. "SOME PROPERTIES OF FERROELECTRICS SUBJECTED TO A STEADY STATE TEMPERATURE GRADIENT." International Journal of Modern Physics B 04, no. 03 (March 10, 1990): 501–16. http://dx.doi.org/10.1142/s0217979290000243.

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A new approach to phase transitions in ferroelectrics in nonequilibrium state is given. It has been shown that if a temperature gradient is imposed on a ferroelectric crystal, then the features of the phase transformation become more complex. Using a simple thermodynamic approach we explain the experimentally observed temperature shift of the spontaneous polarization and pyroelectric coefficient, and the substructure of the dielectric response. All these results are compared with other investigation results, a short review of which is given too.

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33

MAHFOUZI, FARZAD, and BRANISLAV K. NIKOLIĆ. "HOW TO CONSTRUCT THE PROPER GAUGE-INVARIANT DENSITY MATRIX IN STEADY-STATE NONEQUILIBRIUM: APPLICATIONS TO SPIN-TRANSFER AND SPIN-ORBIT TORQUES." SPIN 03, no. 02 (June 2013): 1330002. http://dx.doi.org/10.1142/s2010324713300028.

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Experiments observing spin density and spin currents (responsible for, e.g., spin-transfer torque) in spintronic devices measure only the nonequilibrium contributions to these quantities, typically driven by injecting unpolarized charge current or by applying external time-dependent fields. On the other hand, theoretical approaches to calculate these quantities operate with both the nonequilibrium (carried by electrons around the Fermi surface) and the equilibrium (carried by the Fermi sea electrons) contributions to them. Thus, an unambiguous procedure should remove the equilibrium contributions, thereby rendering the nonequilibrium ones which are measurable and satisfy the gauge-invariant condition according to which expectation values of physical quantities should not change when electric potential everywhere is shifted by a constant amount. Using the framework of nonequilibrium Green functions, we delineate such procedure which yields the proper gauge-invariant nonequilibrium density matrix in the linear-response and elastic transport regime for current-carrying steady state of an open quantum system connected to two macroscopic reservoirs. Its usage is illustrated by computing: (i) conventional spin-transfer torque (STT) in asymmetric F/I/F magnetic tunnel junctions (MTJs); (ii) unconventional STT in asymmetric N/I/F semi-MTJs with the strong Rashba spin–orbit coupling (SOC) at the I/F interface and injected current perpendicular to that plane; and (iii) current-driven spin density within a clean ferromagnetic Rashba spin-split two-dimensional electron gas (2DEG) which generates SO torque in laterally patterned N/F/I heterostructures when such 2DEG is located at the N/F interface and injected charge current flows parallel to the plane. We also compare our results for these three examples with those that would be obtained using improper expressions for the density matrix, which are often found in the literature but which arbitrarily mix nonequilibrium and equilibrium expectation values due to a violation of the gauge invariance.

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34

Zhang, Dongliang, and Qi Ouyang. "Nonequilibrium Thermodynamics in Biochemical Systems and Its Application." Entropy 23, no. 3 (February 25, 2021): 271. http://dx.doi.org/10.3390/e23030271.

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Living systems are open systems, where the laws of nonequilibrium thermodynamics play the important role. Therefore, studying living systems from a nonequilibrium thermodynamic aspect is interesting and useful. In this review, we briefly introduce the history and current development of nonequilibrium thermodynamics, especially that in biochemical systems. We first introduce historically how people realized the importance to study biological systems in the thermodynamic point of view. We then introduce the development of stochastic thermodynamics, especially three landmarks: Jarzynski equality, Crooks’ fluctuation theorem and thermodynamic uncertainty relation. We also summarize the current theoretical framework for stochastic thermodynamics in biochemical reaction networks, especially the thermodynamic concepts and instruments at nonequilibrium steady state. Finally, we show two applications and research paradigms for thermodynamic study in biological systems.

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35

Rodrigues, C. Gonçalves, and R. Luzzi. "Ultrafast dynamics of carriers and phonons of photoinjected double-plasma in aluminium nitride." Revista Mexicana de Física 67, no. 2 Mar-Apr (July 15, 2021): 318–23. http://dx.doi.org/10.31349/revmexfis.67.318.

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Aluminum nitride is attracting great interest of the industry and scientific community due to its interesting properties. In this paper is performed a theoretical study on the ultrafast transient transport properties of photoinjected carriers in wurtzite AlN subjected to electric fields up to 80 kV/cm. For this, the Nonequilibrium Statistical Operator Method was used. The evolution towards the steady state of drift velocity of carriers (electrons and holes) and nonequilibrium temperature (carriers and phonons) subpicosecond scale were determined.

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36

Heinen, Laura, and Andreas Walther. "Programmable dynamic steady states in ATP-driven nonequilibrium DNA systems." Science Advances 5, no. 7 (July 2019): eaaw0590. http://dx.doi.org/10.1126/sciadv.aaw0590.

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Inspired by the dynamics of the dissipative self-assembly of microtubules, chemically fueled synthetic systems with transient lifetimes are emerging for nonequilibrium materials design. However, realizing programmable or even adaptive structural dynamics has proven challenging because it requires synchronization of energy uptake and dissipation events within true steady states, which remains difficult to orthogonally control in supramolecular systems. Here, we demonstrate full synchronization of both events by ATP-fueled activation and dynamization of covalent DNA bonds via an enzymatic reaction network of concurrent ligation and cleavage. Critically, the average bond ratio and the frequency of bond exchange are imprinted into the energy dissipation kinetics of the network and tunable through its constituents. We introduce temporally and structurally programmable dynamics by polymerization of transient, dynamic covalent DNA polymers with adaptive steady-state properties in dependence of ATP fuel and enzyme concentrations. This approach enables generic access to nonequilibrium soft matter systems with adaptive and programmable dynamics.

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37

OGUSHI, FUMIKO, SATOSHI YUKAWA, and NOBUYASU ITO. "DYNAMICS AND STRUCTURE OF GAS-LIQUID INTERFACE." International Journal of Modern Physics B 21, no. 23n24 (September 30, 2007): 4030–34. http://dx.doi.org/10.1142/s0217979207045153.

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The structure and the dynamics of the gas-liquid phase interface of the three-dimensional Lennard-Jones (12-6) particle system are studied using nonequilibrium molecular dynamics simulation. Heat flux maintains the system into a gas-liquid coexisting state with a steady interface. In the steady state, the interface shows an asymmetric structure and this is well described by a free energy density model with an asymmetric double-well form. When the system approaches to the steady state, a gas of the temperature profile appears between each phase and the gap value is relaxed to that in the steady state following [Formula: see text] for large t . It is observed that heat resistance exists in gas-liquid interface in this scale.

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38

da SILVA, P. C., M. L. LYRA, U. L. FULCO, and L. R. da SILVA. "RECURSIVE SEARCH METHOD APPLIED TO A NONEQUILIBRIUM PHASE TRANSITION." International Journal of Modern Physics C 15, no. 02 (February 2004): 233–39. http://dx.doi.org/10.1142/s0129183104005632.

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In this work, we extend the recursive search method to locate the critical point and to obtain the relevant critical exponents of a nonequilibrium phase transition. In particular, the method is applied to the contact process which presents a nonequilibrium phase transition between a steady active to a single inactive absorbing state belonging to the directed percolation universality class. We present the appropriate scaling analysis which allows for precise estimates of the critical parameters with a relatively small computational effort. The proposed scheme can be directly applied to general model systems presenting nonequilibrium transitions into absorbing states including reaction–diffusion and pair contact processes.

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39

Yuge, Tatsuro, and Ayumu Sugita. "A Perturbative Method for Nonequilibrium Steady State of Open Quantum Systems." Journal of the Physical Society of Japan 84, no. 1 (January 15, 2015): 014001. http://dx.doi.org/10.7566/jpsj.84.014001.

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40

Jin, Xiao, and Hao Ge. "Nonequilibrium steady state of biochemical cycle kinetics under non-isothermal conditions." New Journal of Physics 20, no. 4 (April 13, 2018): 043030. http://dx.doi.org/10.1088/1367-2630/aab8cf.

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41

Qian, Hong. "Open-System Nonequilibrium Steady State: Statistical Thermodynamics, Fluctuations, and Chemical Oscillations." Journal of Physical Chemistry B 110, no. 31 (August 2006): 15063–74. http://dx.doi.org/10.1021/jp061858z.

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42

Campa, Alessandro, Shamik Gupta, and Stefano Ruffo. "Nonequilibrium inhomogeneous steady state distribution in disordered, mean-field rotator systems." Journal of Statistical Mechanics: Theory and Experiment 2015, no. 5 (May 15, 2015): P05011. http://dx.doi.org/10.1088/1742-5468/2015/05/p05011.

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43

Meerson, Baruch, Pavel V. Sasorov, and Arkady Vilenkin. "Nonequilibrium steady state of a weakly-driven Kardar–Parisi–Zhang equation." Journal of Statistical Mechanics: Theory and Experiment 2018, no. 5 (May 1, 2018): 053201. http://dx.doi.org/10.1088/1742-5468/aabbcc.

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44

Attard, Phil. "Statistical mechanical theory for steady state systems. V. Nonequilibrium probability density." Journal of Chemical Physics 124, no. 22 (June 14, 2006): 224103. http://dx.doi.org/10.1063/1.2203069.

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45

Ness, Hervé. "Nonequilibrium Thermodynamics and Steady State Density Matrix for Quantum Open Systems." Entropy 19, no. 4 (April 2, 2017): 158. http://dx.doi.org/10.3390/e19040158.

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46

Baranyai, András, and Peter T. Cummings. "Steady state simulation of planar elongation flow by nonequilibrium molecular dynamics." Journal of Chemical Physics 110, no. 1 (January 1999): 42–45. http://dx.doi.org/10.1063/1.478082.

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47

Kamide, Kenji, and Tetsuo Ogawa. "Semiclassical theory for a nonequilibrium steady state in microcavity semiconductor lasers." physica status solidi (c) 8, no. 4 (February 18, 2011): 1250–53. http://dx.doi.org/10.1002/pssc.201000855.

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48

del Junco, Clara, Laura Tociu, and Suriyanarayanan Vaikuntanathan. "Energy dissipation and fluctuations in a driven liquid." Proceedings of the National Academy of Sciences 115, no. 14 (March 16, 2018): 3569–74. http://dx.doi.org/10.1073/pnas.1713573115.

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Minimal models of active and driven particles have recently been used to elucidate many properties of nonequilibrium systems. However, the relation between energy consumption and changes in the structure and transport properties of these nonequilibrium materials remains to be explored. We explore this relation in a minimal model of a driven liquid that settles into a time periodic steady state. Using concepts from stochastic thermodynamics and liquid state theories, we show how the work performed on the system by various nonconservative, time-dependent forces—this quantifies a violation of time reversal symmetry—modifies the structural, transport, and phase transition properties of the driven liquid.

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Gelin, M. F., and D. S. Kosov. "Asymptotic nonequilibrium steady-state operators." Physical Review E 80, no. 2 (August 11, 2009). http://dx.doi.org/10.1103/physreve.80.022101.

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Dettmer, Simon L., H. Chau Nguyen, and Johannes Berg. "Network inference in the nonequilibrium steady state." Physical Review E 94, no. 5 (November 10, 2016). http://dx.doi.org/10.1103/physreve.94.052116.

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