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We propose an extension of the principle of virtual work of mechanics torandom dynamics of mechanical systems. The total virtual work of theinteracting forces and inertial forces on every particle of the system iscalculated by considering the motion of each particle. Then according to theprinciple of Lagrange-d'Alembert for dynamical equilibrium, the vanishingensemble average of the virtual work gives rise to the thermodynamicequilibrium state with maximization of thermodynamic entropy. This approachestablishes a close relationship between the maximum entropy approach forstatistical mechanics and a fundamental principle of mechanics, and constitutesan attempt to give the maximum entropy approach, considered by many as only aninference principle based on the subjectivity of probability and entropy, thestatus of fundamental physics law.

Seeing maximum entropy from the principle of virtual work