[Enthalpy]

PETP is also produced from dimethyl terephthalate reacting with ethylene glycol, in which case any enthalpy change must be tiny, as the reaction replaces an alcohol plus ester by an other alcohol plus ester pair. At least then, removal of methanol looks like the driving force that pushes the first reaction step.

The second reaction step is also a transesterification, where glycol is distilled off.

[pgk]

As a reminder, do not forget that entropy dramatically decreases during PET polymerization due to the formation of one highly long molecule with low flexibility by condensation of many small monomers and therefore, the free energy might finally be positive.

[Corribus]

Removal of one of the products (water or methanol) certainly helps drive the reaction forward, by lowering the statistical likelihood of a backward reaction event from occurring. You would not be able to form long polymers without this important aspect. You can, incidentally, drive even otherwise unfavorable reactions this way. But this is all kinetics and therefore is not, in the rigorous sense, related to a thermodynamic driving force.

It's hard to measure reaction enthalpies for polymerizations. I can't find a value for PET to settle the issue. Ultimately, it depends on what you mean for driving force. I think we can pretty much agree there is no thermodynamic driving force from entropy. A rough calculation shows there may be a driving force in the positive direction by a negative enthalpy change. I concede that this degree of exothermicity may be small enough to be inconsequential, and therefore polymerization in this case would be strictly kinetically controlled (e.g., via removal of a product during the course of the reaction).  The kinetic aspects of polymerization may supercede thermodynamic considerations, no matter what the driving force is.

As a result of the confusion here, I submit that a better title for this thread would have been "Why does PET polymerize?" rather than one that uses a word like driving force, that implies a thermodynamic stimulus.

[Enthalpy]

[...] highly long molecule with low flexibility [...]

Longer molecules tend to have a higher heat capacity per mass unit than shorter ones. This is because they have vibration modes at lower frequencies, which are excited at a lower temperature hence store heat, for instance at room temperature.

The lower resonance frequency results from a bigger mass and compliance per molecule.

Compare for instance ethane and ethylene at room temperature:
Cp=53J/mol/K and Cp=43J/mol/K (from Air Liquide)
with polyethylene:
Cp=31J/K per mol of -CH₂-
http://www.nist.gov/data/PDFfiles/jpcrd178.pdf

The extreme case are metals, where molecules are big enough to grant 3 degrees of vibration freedom to each atom, resulting in 3*RT/mol heat capacity.

[pgk]

Apart the heat capacity, vibration freedom (rotation freedom) is also a question of polymer rigidity/flexibility. Thus, poly(ethylene terephthalate), [PET] is less flexible than poly(ethylene succinate), [PES] and poly(ethylene adipate), [PEA] but less rigid than poly(p-phenylene diamide terephthalate), [Kevlar].

[Enthalpy]

Vibration freedom that stores heat in a long chain does not need the freedom to rotate a full turn around a bond: in a molecule big enough, the rotation compliance and inertia sums over many bonds, which suffices to make the mode's energy accessible to room temperature.

The heat capacity goes even the other direction, since vibrations store RT while rotations store only RT/2.

[pgk]

Question 1: Does the formation of one big molecule from condensation of a great number of small molecules, decrease entropy, Yes or No?
Question 2: Does polymer chain rigidity, decrease entropy, Yes or No?
Question 3: Are all above overcome by heat capacity increasing,Yes or No?

[Enthalpy]

Q1: you get confused with gases where PV determines many things.
Q2&3: apparently you don't understand that rigid molecules vibrate.

[pgk]

You are probably right. So, I have to go back to my Physical Chemistry textbook.
Meanwhile, can you answer my questions by a Yes or by a No?

[pgk]

Meanwhile, I have read in my old Physical Chemistry textbook that entropy is directly associated with the heat capacity, if volume is the only variable of the system that changes when the heat is supplied. But during polymerizations, a plethora of variables might change simultaneously, e.g. the number of moles n, during chain growth, disappearance of the initial H-bonds and creation of different new ones during polyesterification and polytransterification, creation of Van der Waals forces between polymer chains, even changes of the matter state from gas to solid during polyethylene formation, etc. As a  conclusion, entropy cannot directly be associated with the heat capacity during polymerization, regardless if gaseous or liquid monomers are involved.
I have also read in my old Physical Chemistry textbook that indeed rigid molecules vibrate, too. But given that PET rigidity is due to the aromatic rings, I have also read in my old Organic Chemistry textbook that the aromatic rings are planar and that aromatic bonds are shorter than single bonds. As a consequence, benzene ring vibrates at a shorter distance and only in two directions. And as a conclusion, the thermal movements of the overall polymer molecule are quite restricted by the rigid benzene ring vibrations, when compared with the flexible cyclohexane ring vibrations.
However, the discussion went too far and dived into the deep waters of Theoretical Physical Chemistry. In terms of practice, the answer of the initial question is:
“The driving force for PET polymerization is the Le Chatelier principle.”