Question

Free Energy Landscape - Construction and meaning?

Answer 1

Hey mate ^_^

The free energy landscape with respect to ss is a decreasing function of ss, so one would conclude the system will try to minimize the size ss (to minimise its free energy), which is not correct...


#Be Brainly❤️

Answer 2

Hello mate here is your answer.

a particle in a harmonic well. There are two coordinates of interest: position xx (with related potential energy via a constant αα) and a fictitious internal coordinate ss (just for explanatory purposes, let us say the size of the particle): further we assume there is an energy related to the size, also quadratic w.r.t to the latter, via a constant γγ.

For simplicity I completely neglect kinetic energy. So, the partition function for such a system would read

Z=∫∞0∫∞−∞exp[−β(γs2+αx2)]dxds=12πβα−−−√πβγ−−−√Z=∫0∞∫−∞∞exp⁡[−β(γs2+αx2)]dxds=12πβαπβγ

From which the free energy at equilibrium follows. At equilibrium, both mean xx and sswill be different from zero.

Now I could be tempted to describe the free energy landscape by fixing the size ss, and calculate the constrained free energy.

The “constrained” partition function reads

Z¯(s)=exp−βγs2πβα−−−√Z¯(s)=exp−βγs2⁡πβα

Hope it helps you.