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Spring Mass System: Total Free Energy

Minimizing the potential energy:

Optical tweezer: Total energy

Finding the maximum of a function f(u):

Express potential energy using Taylor series: and at equilibrium

Express function as Taylor expansion: (solve for f(x)=cos(x))

Free energy (including thermal activities/contribution): (Definition)

Define entropy of a macroscopic and microscopic state:

The equilibrium of the state....


Entropy and hydrophobicity: an example

How many spatial orientation one water molecule could have?

The change in entropy for one water molecule:

The energy cost when n water molecules are next to hydrophobic molecules:

