摘要
We present a fully quantum solution to the Gibbs paradox (GP) with an illustration based on a gedanken experiment with two particles trapped in an infinite potential well. The well is divided into two cells by a solid wall, which could be removed for mixing the particles. For the initial thermal state with correct two-particle wavefunction according to their quantum statistics, the exact calculations show the entropy changes are the same for boson, fermion and non-identical particles. With the observation that the initial unmixed state of identical particles in the conventional presentations actually is not of a thermal equilibrium, our analysis reveals the quantum origin of the paradox, and confirms Jaynes' observation that entropy increase in Gibbs mixing is only due to the including more observables. To further show up the subtle role of the quantum mechanism in the GP, we study the different finite size effect on the entropy change and show the work performed in the mixing process is different for various types of particles.
We present a fully quantum solution to the Gibbs paradox （GP） with an illustration based on a gedanken experiment with two particles trapped in an infinite potential well. The well is divided into two cells by a solid wall, which could be removed for mixing the particles. For the initial thermal state with correct two-particle wavefunction according to their quantum statistics, the exact calculations show the entropy changes are the same for boson, fermion and non-identical particles. With the observation that the initial unmixed state of identical particles in the conventional presentations actually is not of a thermal equilibrium, our analysis reveals the quantum origin of the paradox, and confirms Jaynes＇ observation that entropy increase in Gibbs mixing is only due to the including more observables. To further show up the subtle role of the quantum mechanism in the GP, we study the different finite size effect on the entropy change and show the work performed in the mixing process is different for various types of particles.
基金
supported by the National Natural Science Foundation of China (Grant Nos. 11121403,10935010 and 11074261)
