Does thermodynamics have a hamiltonian?

• Main Author: Thun, Winter Chee Siong.
• Other Authors: Koh Tieh Yong
• Format: Final Year Project
• Language: English
• Published: 2009
• Subjects: DRNTU::Science::Physics::Heat and thermodynamics
• Online Access: http://hdl.handle.net/10356/18030
• Institution: Nanyang Technological University

Thermofluid, it is one of the most complicated dynamic systems known to the mankind since before the “time” was first created. In fact, all the real fluids existing in our universe are thermofluid in their very own nature. Thus we have no choice but trying to understand it as much as we could with any mean we could access to. As Hamiltonian is known for best for its simplicity and adaptability in our classical mechanics, hence this project was founded with the aim to search for the Hamiltonian of the thermodynamic system. The research began with fluid mechanics and the mathematic for Hamiltonian where all types of variation principle was carefully studied & verified. The second phase focused on the current works in thermodynamic Hamiltonian written by Prof. Angel Fierros Palacios. His works were fully analyzed and studied but unfortunately, all of them were proved either trivial or wrong in this research. Moving into the next stage, the Euler-Poisson Equation was rediscovered, together with the finding of General form of Hamiltonian; and the fundamental layout to obey for all the physical system with certain general types of variables if one were to follow the Hamilton’s Principle. Also, instead of getting the answer we want, certain structures of trivial Lagrangians that lead to the error finding of true thermodynamic Lagrangians were found, together with all the corresponding mathematical law. As a conclusion, the search for the thermodynamic Hamiltonian is still at the primitive stage. Its existence is yet to be proven or disproved at the current stage. But the rest of the findings in this project are useful for the future research especially all the mathematical finding.