Recent Advances in Thermo and Fluid Dynamics by Mofid Gorji-Bandpy

By Mofid Gorji-Bandpy

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By a generalization of the Liouville–von Neumann equation, the statistical thermodynamic theory of the ensemble of the damped oscillators in contact with a thermal bath is given. By introducing the quantum entropy of the ensemble, it is shown that the entropy of the ensemble grows in a dissipative process and in thermal equilibrium for the probability distribution of the quantum states, such that Gibbs’ canonical distribution is valid. Finally, a wave equation of the linearly damped oscillator is given.

By the second law of nonequilibrium thermodynamics, the entropy S (U , q ) satisfies the balanced equation: dS dSr dSi = + , dt dt dt dSi ³0 dt (3) d Sr where dt is the reversible rate of change of the entropy or entropy flux on the rigid diathermal dSi wall and dt is the so-called entropy production. 5772/61010 Also, entropy production and the so-called rate of energy dissipation R =T dSi ¶S dq =T ³0 ¶q dt dt (10) decrease the free energy of the oscillator. In what follows, we shall give the actual form of the rate of energy dissipation.

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