By R. Blandford, K. Thorne

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**Additional info for Applications of Classical Physics**

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Practically this means that instead of observing, for instance, many lipid vesicles of identical size at a given time (as it is usually done in most experiments), one can also observe one single vesicle over a long period of time, as it is usually done in simulations of membranes. We will make use of the ergodic theorem in Chapter 8 when we introduce Monte Carlo simulations. Below we will provide an introduction those thermodynamic terms that are important for membranes and the topics discussed in this book.

Let us consider the special case of a symmetric membrane for which the phase problem is relatively simple. The membrane is symmetrical with respect to its center (very reasonable assumption). 11) The term containing the sine function is equal to zero (since sin( x ) = − sin(− x )). The structure factor now is a real function. We also obtain Fu ( R) = | Fu ( R)| · exp(iα) = | Fu ( R)| · cos(α) + i| Fu ( R)| · sin(α). Since the imaginary part is equal to zero, α = n · π. The phase factors therefore display values of ±1.

One can divide thermodynamics into subdisciplines, which are equilibrium thermodynamics, and linear and nonlinear nonequilibrium thermodynamics. Equilibrium thermodynamics deﬁnes relationships between functions of state and the variables, which are strictly true in all ﬁelds of physics of equilibrated systems, from particle physics and quantum mechanics to cosmology. Naturally it is also true for all biological matter that does not undergo rapid changes. Since it is a theory based on ﬁrst principles without approximations, one can derive surprising relations between various observables.

### Applications of Classical Physics by R. Blandford, K. Thorne

by George

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