Seeing maximum entropy from the principle of virtual work
Résumé
We propose an application of the principle of virtual work of mechanics to random dynamics of mechanical systems. The total virtual work of the interacting forces and inertial forces on every part of the system is calculated by considering the motion of each particle. This calculation leads to a known expression of thermodynamic work in statistical mechanics: the work of a infinitesimal process is the average of the infinitesimal energy variation over all microstates of the system. Then according to the Lagrange-D'Alembert principle, the vanishing virtual work yields stable thermodynamic equilibrium with the maximization of thermodynamic entropy for canonical ensemble. This application reveals a close relationship between the maximum entropy approach for statistical mechanics and a fundamental principle of mechanics. This work is an attempt to give the maximum entropy approach, considered by many as an inference principle based on the subjectivity of probability and entropy, the status of a fundamental physics law.
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