Classical statistical physics and quantum mechanics

Francesco R. Ruggeri

In physics, there are deterministic theories such as classical mechanics and statistical theories such as classical statistical mechanics and quantum mechanics. Many interpretations are applied to statistical theories and there is sometimes debate as to the application of such theories in various physical scenarios. In a previous note, we considered cycling due to exp(iEt) in quantum mechanics and tried to argue that such cycling may also appear in statistical mechanics. We made use of the example of the ground state of the quantum oscillator which has a quantum mechanical density of the same form as the classical statistical mechanical result. In this note, we wish to consider the idea of cycling in statistical mechanics using some simple examples. In addition, we wish to also examine the notion of losing information to pass from a deterministic theory to a statistical one. Finally, we wish to consider some possible aspects of the classical statistical density in a potential. It seems that even in classical statistical mechanics, the picture presented by the ‘averaging’ may actually be quite different from the physical scenario which may contain deterministic behavior which is lost in the calculation of statistical results.

Jean Zinn‐Justin

N. N. Bogolyubov, A. M. Kurbatov, A. S. Shumovskiǐ

Mei Xiaochun

Based on the concept of ensemble, it is proved in the manuscript that the probability amplitude function can also been used to describe the classical statistical system. The motion equations of probability amplitude functions of classical statistical system are obtained, which are similar to that in quantum mechanics. It is also proved in the meantime that microsystems that obey quantum mechanics can also be described in the forms of classical statistical mechanics and deterministic classical mechanics. The quantum revised formula of classical interaction force and the revised Liouville's equations are also obtained. In this way, the transformation of two descriptive forms between classical mechanics and quantum mechanics is achieved. A new and rational interpretation about quantum mechanics, including the meaning of wave function, the potential barrier penetration of microparticles, the Uncertainty relation, the wave-particle duality, the essence of spin and the Bell's inequality and so on, is provided in the paper. Based on the transformation, two fundamental hypotheses are put forward as the basic postulates of classical statistical physics. The equal probability hypothesis in the equilibrium states is given up. The united description of nonequilibrium state mechanics and equilibrium state statistical mechanics is reached, and the so-called reversibility paradox can also be eliminated.

Chen‐Bin Huang, Yong-Chang Huang, Jia-Min Song

Density distribution function of classical statistical mechanics is generally generalized as a product of a general complex function and its complex Hermitian conjugate function, and the average of classical statistical mechanics is generalized as the average of the quantum mechanics. Furthermore, this paper derives three ones of the five axiom presumptions of quantum mechanics, e.g., deduces Schrȍdinger equation by two general ways, makes the three axiom presumptions into three theorems of quantum mechanics, not only solves the crisis to hard understand, but also gets new theories and new discoveries, e.g., this paper solves the crisis of the origin of the wave-particle duality, derives operators, eigenvalues and eigenstates, deduces commutation relations for coordinate and momentum as well as the time and energy, and discovers quantum mechanics is just a generalization ( mechanics ) theory of the complex square root of ( real density function of ) classical statistical mechanics. Quantum mechanics being just a generalization theory of the complex square root of classical statistical mechanics is both new physics and revolutionary discovery, which are affecting people’s deep philosophical thinking for modern physics development, solve all the crisises of quantum mechanics, quantum information and so on, and make quantum mechanics have scientific solid bases being checked and both no basic axiom presumption and no all the quantum strange incomprehensible properties, because classical statistical mechanics and the complex square root of classical statistical mechanics have the scientific solid bases being checked. In addition, this paper discovers the reason no taking the time derivative of space coordinates in Schrȍdinger equation. Therefore, this paper gives solution to the crisis of the first quantization origin, and mainly deduces quantum physics no all the quantum current strange incomprehensible properties.

G. E. Uhlenbeck