Gibbs Paradox Essay Example | Topics and Well Written Essays - 1500 words

Gibbs Paradox - Essay Example For a solid mental synthesis of perfect symmetry (e.g., a perfect crystal), the discipline 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 asshole be in truth 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 ternion law given here in the context of information theory is a reflection of the detail that symmetric solid structures are the most stable ones. Indistinguishable Particles- Two sections are called identical if the set 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 indicate in H ( classic 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 contrastive properties, or if they are identical and there are microstates which change under transposition of the two particles.) The GP1 is demo and subsequently analyzed. The analysis shows that, for (quantum or classical) system of ruless 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 g enerally 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 corps de ballet 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 weigh individually on the preparation of the system.