On a Possible Formulation of Particle Dynamics in Terms of Thermodynamic Conceptualizations and the Role of Entropy In It
NAVAL POSTGRADUATE SCHOOL MONTEREY CA
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It is shown that the laws of particle dynamics can be formulated in a thermodynamic framework. An important role is played by an integrating factor which makes the energy exchange with the environment a total differential and leads to the definition of a mechanical entropy. The integrating factor is shown to be a function of velocity only and an argument following Caratheodorys proves the existence of a unique limiting velocity which makes its appearance in the integrating factor. Equilibrium and stability conditions for dynamic systems are derived and lead to the formulation of dynamics as processes in a space- entropy manifold the metric of which is determined by the nature of the system. The dynamic laws follow from a variational principle. For the case of isentropic processes and with a particular choice of the integrating factor they are shown to be the laws of special relativistic mechanics. More general dynamic processes are discussed.