We present the Jacobi’s second equality in the form of stochastic equation. By the theorem of factorization of the solution of Fokker- Planck equation, the solution of Bloch equation is obtained and using the Matsubara formalism we determine the wave functions of a free particle and harmonic oscillator of the Euclidean quantum mechanic that permitted us to calculate the Leipnik entropy of ours particles. Showing that the joint entropy of the free particle increases with time and for the case of harmonic oscillator it fluctuates with time and frequency.
