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1

Azbel’, M. Ya. "Nonlocal Einstein relation." Physical Review B 46, no. 23 (1992): 15004–7. http://dx.doi.org/10.1103/physrevb.46.15004.

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2

Balucani, U., R. Vallauri, and T. Gaskell. "Generalized Stokes-Einstein Relation." Berichte der Bunsengesellschaft für physikalische Chemie 94, no. 3 (1990): 261–64. http://dx.doi.org/10.1002/bbpc.19900940313.

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3

Nyberg, Svein Olav. "The discrete Einstein relation." Circuits Systems and Signal Processing 16, no. 5 (1997): 547–57. http://dx.doi.org/10.1007/bf01185004.

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4

Renata Freiberg, Uta. "Einstein relation on fractal objects." Discrete & Continuous Dynamical Systems - B 17, no. 2 (2012): 509–25. http://dx.doi.org/10.3934/dcdsb.2012.17.509.

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5

Gradenigo, G., A. Sarracino, D. Villamaina, and A. Vulpiani. "Einstein relation in superdiffusive systems." Journal of Statistical Mechanics: Theory and Experiment 2012, no. 06 (2012): L06001. http://dx.doi.org/10.1088/1742-5468/2012/06/l06001.

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6

Kaganov, M. I., and V. B. Fiks. "Einstein relation for quantum systems." Journal of Statistical Physics 38, no. 1-2 (1985): 329–45. http://dx.doi.org/10.1007/bf01017865.

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7

Hilfer, R., and A. Blumen. "Probabilistic interpretation of the Einstein relation." Physical Review A 37, no. 2 (1988): 578–81. http://dx.doi.org/10.1103/physreva.37.578.

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8

Gradenigo, G., A. Sarracino, D. Villamaina, and A. Vulpiani. "Einstein Relation in Systems with Anomalous Diffusion." Acta Physica Polonica B 44, no. 5 (2013): 899. http://dx.doi.org/10.5506/aphyspolb.44.899.

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9

Baranovskii, S. D., T. Faber, F. Hensel, and P. Thomas. "On the Einstein relation for hopping electrons." Journal of Non-Crystalline Solids 227-230 (May 1998): 158–61. http://dx.doi.org/10.1016/s0022-3093(98)00031-3.

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10

Tian, Yong, and Chung-Ming Ko. "Mass discrepancy–acceleration relation in Einstein rings." Monthly Notices of the Royal Astronomical Society 472, no. 1 (2017): 765–71. http://dx.doi.org/10.1093/mnras/stx2056.

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11

Cappelezzo, M., C. A. Capellari, S. H. Pezzin, and L. A. F. Coelho. "Stokes-Einstein relation for pure simple fluids." Journal of Chemical Physics 126, no. 22 (2007): 224516. http://dx.doi.org/10.1063/1.2738063.

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12

Debberma, M. "Quantized Semiconductor Superlattices and the Einstein Relation." Journal of Nanoengineering and Nanomanufacturing 6, no. 1 (2016): 15–32. http://dx.doi.org/10.1166/jnan.2016.1261.

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13

Donhee Ham and A. Hajimiri. "Virtual damping and einstein relation in oscillators." IEEE Journal of Solid-State Circuits 38, no. 3 (2003): 407–18. http://dx.doi.org/10.1109/jssc.2002.808283.

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14

Guidoni, S. E., and C. M. Aldao. "On diffusion, drift and the Einstein relation." European Journal of Physics 23, no. 4 (2002): 395–402. http://dx.doi.org/10.1088/0143-0807/23/4/302.

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15

Parker, Leonard, and Alpan Raval. "Relation between Einstein and quantum field equations." Physical Review D 57, no. 12 (1998): 7327–39. http://dx.doi.org/10.1103/physrevd.57.7327.

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16

Chakraborty, D., M. V. Gnann, D. Rings, et al. "Generalised Einstein relation for hot Brownian motion." EPL (Europhysics Letters) 96, no. 6 (2011): 60009. http://dx.doi.org/10.1209/0295-5075/96/60009.

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17

Barkai, E., and V. N. Fleurov. "Generalized Einstein relation: A stochastic modeling approach." Physical Review E 58, no. 2 (1998): 1296–310. http://dx.doi.org/10.1103/physreve.58.1296.

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18

Baranovskii, S. D., T. Faber, F. Hensel, and P. Thomas. "On the Einstein Relation for Hopping Electrons." physica status solidi (b) 205, no. 1 (1998): 87–90. http://dx.doi.org/10.1002/(sici)1521-3951(199801)205:1<87::aid-pssb87>3.0.co;2-p.

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19

Ghatak, K. P., N. Chattopadhyay, and M. Mondal. "The Einstein relation in Kane‐type semiconductors." Journal of Applied Physics 63, no. 9 (1988): 4536–39. http://dx.doi.org/10.1063/1.340151.

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20

BISWAS, S. N., and K. P. GHATAK. "The Einstein relation in zero-gap semiconductors." International Journal of Electronics 73, no. 2 (1992): 287–93. http://dx.doi.org/10.1080/00207219208925666.

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21

Havlin, S. "Range of validity of the Einstein relation." Physical Review Letters 55, no. 1 (1985): 130. http://dx.doi.org/10.1103/physrevlett.55.130.

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22

Khrapak, Sergey. "Stokes–Einstein relation in simple fluids revisited." Molecular Physics 118, no. 6 (2019): e1643045. http://dx.doi.org/10.1080/00268976.2019.1643045.

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23

Gonçalves, Patrícia, and Milton Jara. "The Einstein Relation for the KPZ Equation." Journal of Statistical Physics 158, no. 6 (2014): 1262–70. http://dx.doi.org/10.1007/s10955-014-1158-9.

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24

Peng, Y. Q., J. H. Yang, F. P. Lu, et al. "Einstein relation in chemically doped organic semiconductors." Applied Physics A 86, no. 2 (2006): 225–29. http://dx.doi.org/10.1007/s00339-006-3747-1.

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25

González, J., and D. Jou. "Extended thermodynamics and the nonequilibrium Einstein relation." Physics Letters A 168, no. 5-6 (1992): 375–77. http://dx.doi.org/10.1016/0375-9601(92)90521-m.

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26

Vasconcellos, Áurea Rosas, Roberto Luzzi, and Leopoldo S. García-Colin. "Diffusion and mobility and generalized Einstein relation." Physica A: Statistical Mechanics and its Applications 221, no. 4 (1995): 495–510. http://dx.doi.org/10.1016/0378-4371(95)00164-6.

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27

Evoy, Erin, Adrian M. Maclean, Grazia Rovelli, et al. "Predictions of diffusion rates of large organic molecules in secondary organic aerosols using the Stokes–Einstein and fractional Stokes–Einstein relations." Atmospheric Chemistry and Physics 19, no. 15 (2019): 10073–85. http://dx.doi.org/10.5194/acp-19-10073-2019.

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Abstract. Information on the rate of diffusion of organic molecules within secondary organic aerosol (SOA) is needed to accurately predict the effects of SOA on climate and air quality. Diffusion can be important for predicting the growth, evaporation, and reaction rates of SOA under certain atmospheric conditions. Often, researchers have predicted diffusion rates of organic molecules within SOA using measurements of viscosity and the Stokes–Einstein relation (D∝1/η, where D is the diffusion coefficient and η is viscosity). However, the accuracy of this relation for predicting diffusion in SOA
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28

Jungemann, C., B. Neinhüs, and B. Meinerzhagen. "Investigation of the Local Force Approximation in Numerical Device Simulation by Full-band Monte Carlo Simulation." VLSI Design 13, no. 1-4 (2001): 281–85. http://dx.doi.org/10.1155/2001/10378.

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The critical assumptions in the drift-diffusion model are the local force approximation and the use of the Einstein relation under nonequilibrium conditions. The validity of these two approximations is investigated by full-band Monte Carlo simulation for a SiGe-HBT. It is found that neither the local force approximation nor the Einstein relation holds. Even Einstein relations generalized with the local temperature fail under quasiballistic transport conditions, indicating that the energy transport and hydrodynamic approach are also problematic.
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29

Zakari, M., and D. Jou. "A generalized Einstein relation for flux-limited diffusion." Physica A: Statistical Mechanics and its Applications 253, no. 1-4 (1998): 205–10. http://dx.doi.org/10.1016/s0378-4371(97)00654-7.

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30

Abou, Bérengère, François Gallet, Pascal Monceau, and Noëlle Pottier. "Generalized Einstein Relation in an aging colloidal glass." Journal of Non-Newtonian Fluid Mechanics 149, no. 1-3 (2008): 3–8. http://dx.doi.org/10.1016/j.jnnfm.2007.05.009.

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31

Tomboulis, E. T. "Exact relation between Einstein and quadratic quantum gravity." Physics Letters B 389, no. 2 (1996): 225–30. http://dx.doi.org/10.1016/s0370-2693(96)01293-2.

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32

Komorowski, T., and S. Olla. "Einstein relation for random walks in random environments." Stochastic Processes and their Applications 115, no. 8 (2005): 1279–301. http://dx.doi.org/10.1016/j.spa.2005.03.009.

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33

Nguyen, Thanh H., and Stephen K. O’Leary. "Einstein relation for disordered semiconductors: A dimensionless analysis." Journal of Applied Physics 98, no. 7 (2005): 076102. http://dx.doi.org/10.1063/1.2060961.

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34

Corsaro, C., E. Fazio, and D. Mallamace. "The Stokes-Einstein relation in water/methanol solutions." Journal of Chemical Physics 150, no. 23 (2019): 234506. http://dx.doi.org/10.1063/1.5096760.

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35

Balboa Usabiaga, Florencio, Xiaoyi Xie, Rafael Delgado-Buscalioni, and Aleksandar Donev. "The Stokes-Einstein relation at moderate Schmidt number." Journal of Chemical Physics 139, no. 21 (2013): 214113. http://dx.doi.org/10.1063/1.4834696.

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36

Franz, Astrid, Christian Schulzky, and Karl Heinz Hoffmann. "The Einstein relation for finitely ramified Sierpinski carpets." Nonlinearity 14, no. 5 (2001): 1411–18. http://dx.doi.org/10.1088/0951-7715/14/5/324.

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37

Abou, Bérengère, François Gallet, Pascal Monceau, and Noëlle Pottier. "Generalized Einstein Relation in an aging colloidal glass." Physica A: Statistical Mechanics and its Applications 387, no. 14 (2008): 3410–22. http://dx.doi.org/10.1016/j.physa.2008.02.034.

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38

Pal, J., M. Debbarma, N. Debbarma, and M. Mitra. "The Einstein Relation in Field Aided Semiconductor Superlattices." Advanced Science, Engineering and Medicine 11, no. 10 (2019): 953–70. http://dx.doi.org/10.1166/asem.2019.2440.

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39

Guo, Xiaoqin. "Einstein relation for random walks in random environment." Annals of Probability 44, no. 1 (2016): 324–59. http://dx.doi.org/10.1214/14-aop975.

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40

O’Malley, T. F. "Einstein relation for electrons in high-density argon." Physical Review A 36, no. 6 (1987): 2838–41. http://dx.doi.org/10.1103/physreva.36.2838.

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41

Balucani, Umberto, Günther Nowotny, and Gerhard Kahl. "The generalized Stokes - Einstein relation for liquid sodium." Journal of Physics: Condensed Matter 9, no. 16 (1997): 3371–76. http://dx.doi.org/10.1088/0953-8984/9/16/009.

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42

Wei, Yi, Xu Zhou, Yingquan Peng, Ying Tang, Ying Wang, and Sunan Xu. "Generalized Einstein relation for co-doped organic semiconductors." Journal of Applied Physics 118, no. 12 (2015): 125501. http://dx.doi.org/10.1063/1.4931424.

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43

Mansouri, E., J. Karamdel, M. T. Ahmadi, and M. Berahman. "Electrical conductivity and Einstein relation modeling in phosphorene." International Journal of Modern Physics B 33, no. 06 (2019): 1950033. http://dx.doi.org/10.1142/s0217979219500334.

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Investigation on (2-dimensional) (2D) materials is growing significantly due to the fundamental electronic properties in the direct inherent bandgap, higher carrier mobility, and easier exfoliation. Phosphorene as a new 2D configuration has presented excellent potential in electronic and optoelectronic applications. In this study, the conductivity of monolayer phosphorene and Einstein’s relations as fundamental parameters in semiconductor manufacturing are analytically modeled. In addition, dependency of conductivity on normalized Fermi energy ([Formula: see text]) is demonstrated. According t
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44

Liu, Bin, and John Goree. "Test of the Einstein Relation in Dusty Plasmas." IEEE Transactions on Plasma Science 44, no. 4 (2016): 483–86. http://dx.doi.org/10.1109/tps.2015.2467966.

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45

Li, Ling, Gregor Meller, and Hans Kosina. "Einstein relation in hopping transport of organic semiconductors." Journal of Applied Physics 106, no. 1 (2009): 013714. http://dx.doi.org/10.1063/1.3159654.

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46

Telcs, András. "The Einstein Relation for Random Walks on Graphs." Journal of Statistical Physics 122, no. 4 (2006): 617–45. http://dx.doi.org/10.1007/s10955-005-8002-1.

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47

Uribe, F. J., and R. M. Velasco. "Einstein Relation for Electrons in an Electric Field." Journal of Statistical Physics 162, no. 1 (2015): 242–66. http://dx.doi.org/10.1007/s10955-015-1386-7.

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48

Schonmann, Roberto H. "Einstein Relation for a Class of Interface Models." Communications in Mathematical Physics 232, no. 2 (2003): 279–302. http://dx.doi.org/10.1007/s00220-002-0749-5.

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49

Peng, Y. Q., J. H. Yang, and F. P. Lu. "Generalization of Einstein relation for doped organic semiconductors." Applied Physics A 83, no. 2 (2006): 305–11. http://dx.doi.org/10.1007/s00339-006-3488-1.

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50

Boldrighini, C., and M. Soloveitchik. "On the Einstein relation for a mechanical system." Probability Theory and Related Fields 107, no. 4 (1997): 493–515. http://dx.doi.org/10.1007/s004400050095.

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