Author(s)

Aleksey M. Avdeenko

Department of Information Technology, The National Research Technological University, Moscow, Russia.

The approach proposed in the study is based on the revision of the concept of time as a point on the real axis. It uses the concept of fuzzy time as the set of real numbers with a finite, but not equal to one, function of membership to the time set, i.e. the fuzzy time concept. It is postulated that in fuzzy time t the system dynamics follows from the standard variational principle of the least action and is ordinary Hamilton-Jacobi mechanics. This validates the passage to the limit from fuzzy mechanics to ordinary variational conservative mechanics. The Liouville equation is solved by the method of successive approximations in the time domain of a much larger characteristic scale of fuzziness, using interaction as a small parameter. A standard diagram technique is used. It can be shown that the defuzzification of the Liouville equation inevitably reduces the reversible part in the description to the irreversible evolutionary equation. The latter leads to the second law of thermodynamics. Generalization to the quantum case is possible, i.e. the so-called fuzzy Pauli equation can be drawn.

Fuzzy Sets, Fuzzy Time, Master Equation, Second Law of Ther-modynamics, Fuzzy Pauli Equation

Avdeenko, A. (2018) The Master Equation and the Pauli Equation in the Fuzzy Time Model. Journal of Applied Mathematics and Physics, 6, 358-372. doi: 10.4236/jamp.2018.62034.