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35
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12144284371
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note
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Evans and Hanley also added the term -Script P Sign dν on the right-hand side of Eq. (1) to discuss the pressure Script P Sign as an energy response to a change of the volume νV in shear flow, by analogy with equilibrium thermodynamics. However, it is not evident that we: can justify such a term in nonequilibrium steady states at the level of the theory presented here. We mention some problems with the discussion of the pressure briefly in Sec. VI. In this paper, we mainly concentrate on the fixed volume case where dν=0.
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40
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0001080621
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H. Mori, Phys. Rev. 112, 1829 (1958).
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translated from Russian by P. J. Shepherd (Consultants Bureau, New York)
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D. N. Zubarev, Nonequilibrium Statistical Thermodynamics, translated from Russian by P. J. Shepherd (Consultants Bureau, New York, 1974).
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47
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Toda, M.2
Hashitsume, H.3
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58
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12144258140
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note
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(mov)(τ) is the phase-space momentum justified by the Lagrangian formalism, while the momentum used in the Dolls tensor dynamics is the thermal momentum, namely the mass times the velocity in the moving frame (defined by the global velocity profile).
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59
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0004270407
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translated from the Russian by J. B. Sykes and J. S. Bell (Pergamon Press, Oxford)
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0004056428
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translated from the Russian by J. B. Sykes and M. J. Kearsley (Pergamon Press, Oxford)
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L. D. Landau and E. M. Lifshitz, Statistical Physics, translated from the Russian by J. B. Sykes and M. J. Kearsley (Pergamon Press, Oxford, 1968).
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Statistical Physics
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Landau, L.D.1
Lifshitz, E.M.2
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65
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12144250680
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note
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Equation (22) is a well known relation in equilibrium thermodynamics, but it is not obvious in nonequilibrium states such as shear flows. This is the reason why the definition of the temperature is still important in statistical mechanics. For example, see Refs. [77-79] for other attempts to define a temperature dynamically. Evans and Hanley used Eq. (22) as the definition of the temperature to discuss their shear flow thermodynamics [32], whereas Eq. (22) is the result obtained from the canonical distribution approach in this paper.
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66
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12144261996
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note
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The divergence of a nonequilibrium entropy in a steady shear flow in thermostated dynamics has been considered; for example, see Ref. [35]. However, note that the explanation for the entropy divergence in that case is different from that used here.
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67
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12144272551
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note
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3=-1n ≡ -1, we obtain the form (19) for the canonical distribution for shear flow.
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78
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0004145975
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North-Holland Publishing Company, Amsterdam
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C. J. Joachain, Quantum Collision Theory (North-Holland Publishing Company, Amsterdam, 1975).
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Joachain, C.J.1
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