Gibbs Paradox - Essay Example

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This paper contains a deeply analyzed report about Gibbs Paradox along with its relationship with different theories like Information theory and thermodynamic entropy. In statistical mechanics, a simple derivation of the entropy of an ideal gas based on the Boltzmann distribution yields an expression for the entropy which is not extensive…
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Gibbs Paradox
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Download file to see previous pages : For a solid structure of perfect symmetry (e.g., a perfect crystal), the information I is zero and the (information theory) entropy S is at the maximum. If entropy change is information loss, ?S = ??I , the conservation of L can be very easily satisfied, ?L = ?S + ?I = 0 . Another form of the second law of information theory is: the entropy S of the universe tends toward a maximum. The second law given here can be taken as a more general expression of the Curie-Rosen symmetry principle [5,6]. The third law given here in the context of information theory is a reflection of the fact that symmetric solid structures are the most stable ones. Indistinguishable Particles:- Two particles are called identical if the values of all their inner attributes agree. H must be so constituted that the transposition of two identical particles is defined for every vector in H (quantum case) or every phase space point in H (classical case), respectively. Two identical particles are called indistinguishable if every pure quantum state (every classical microstate) is invariant under transposition of these two particles; otherwise the two particles are called distinguishable. Two non-identical particles are always considered distinguishable. Resolution of the paradox in terms of Indistinguishable particles:- In the preceding section as I discussed about indistinguishable particles (Two particles are said to be indistinguishable if they are either non-identical, that is, if they have different properties, or if they are identical and there are microstates which change under transposition of the two particles.) The GP1 is demonstrated and subsequently analyzed. The analysis shows that, for (quantum or classical) systems of distinguishable particles, it is generally uncertain of which...
The GP1 is demonstrated and subsequently analyzed. The analysis shows that, for (quantum or classical) systems of distinguishable particles, it is generally uncertain of which particles they consist. The neglect of this uncertainty is the root of the GP1. For the statistical description of a system of distinguishable particles, an underlying set of particles, containing all particles that in principle qualify for being part of the system, is assumed to be known. Of which elements of this underlying particle set the system is composed differs from microstate to microstate. Thus, the system is described by an ensemble of possible particle compositions. The uncertainty about the particle composition contributes to the entropy of the system. Systems for which all possible particle compositions are equiprobable will be called harmonic. Classical systems of distinguishable identical particles are harmonic as a matter of principle; quantum or classical systems of non-identical particles are not necessarily harmonic, since for them the composition probabilities depend individually on the preparation of the system. ...Download file to see next pagesRead More
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