By Bachmann M.
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Extra resources for Thermodynamics and statistical mechanics of polymers and proteins
If |ψ0 is normalized, the real number |cn |2 = an |ψ0 an |ψ0 ⋆ is interpreted as the probability that the system is in the nth ˆ Since the system must be in any eigenstate |an after the measurement of A. eigenstate of Aˆ after the measurement, n |cn |2 = 1. An average or expectation ˆ 0 . value is obtained as Aˆ = n an |cn |2 = ψ0 |A|ψ The uncertainty principle causes that our information, even after “preparation” of a system state, must remain incomplete. This is because two Hermitean operaˆ=B ˆ Aˆ and thus the result of the simultanetors do not necessarily commute AˆB ous measurement depends on the order of operations.
Thus, in the thermodynamic limit, the canonical and the microcanonical ensemble yield identical quantitative informations about the thermodynamic behavior of the system. The Grand Canonical Ensemble Another frequently required demand is the fluctuation of the number of particles N in the system and to keep the chemical potential µ constant. This is the physical situation which is statistically provided by the grand canonical ensemble. We have already introduced the constraints with respect to the normalization of the microstate probability and the constant mean value of energy.
In the globular phase, however, the attractive van der Waals forces between many atoms of the monomers, that stabilize the globular shapes, are necessarily to be taken into account in order to describe the formation of compact structures correctly. , many atoms are involved, it is sufficient to introduce a general “hydrophobic” interaction between abstractified “united atoms” which comprise subsets of atoms. Thus, the effect can be qualitatively and, for large systems, even quantitatively be described by a simplified, coarse-grained model that in addition to the system constraints only includes an effective interaction among nonbonded monomers.