By differentiating the defining equations for H, A and G and combining the results with equation (A2.T25) and equation (A2.T27) for dU and U (which are repeated here) one obtains general expressions for the differentials dH, dA, dG and others. One differentiates the defined quantities on the left-hand side of equation (A2.1.34), equation (A2.1.35), equation (A2.1.36), equation (A2.1.37), equation (A2.1.38) and equation (A2.1.39) and then substitutes die right-hand side of equation (A2.1.33) to obtain the appropriate differential. These are examples of Legendre transformations. ... [Pg.347]

fluctuation dissipation theorem relates the dissipative part of the response fiinction (x") to the correlation of fluctuations (A, for any system in themial equilibrium. The left-hand side describes the dissipative behaviour of a many-body system all or part of the work done by the external forces is irreversibly distributed mto the infinitely many degrees of freedom of the themial system. The correlation fiinction on the right-hand side describes the maimer m which a fluctuation arising spontaneously in a system in themial equilibrium, even in the absence of external forces, may dissipate in time. In the classical limit, the fluctuation dissipation theorem becomes / /., w) = w). [Pg.719]

One way to solve this is to invert the operator on the left hand side, thereby converting this differential equation into an integral equation. The general result is... [Pg.965]

To develop an additional equation, we simply make the ansatz that the first temi on the left-hand side of equation (3.11.215h) equals the first temi on the right-hand side and similarly with the second temi. This innnediately gives us Hamilton s equations... [Pg.1001]

Figure Bl.19.31. AFM image of a 2.7 mn x 2.7 mn area of a polypropylene surfaee, displaying metiiyl groups and right- and left-handed heliees. (Taken from [143]. figure 10.)... |

[Pg.117]

The right-hand side will be treated in a following section VI.E, where we shall see that it is small in the nearly nonrelativistic limit and that it vanishes in the absence of an elechomagnetic field. The left-hand side can be evaluated to give... [Pg.164]

See also in sourсe #XX -- [ Pg.1267 , Pg.2087 ]

See also in sourсe #XX -- [ Pg.103 ]

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