Abstract
We present an extension of Nelsonʼs stochastic quantum mechanics to finite temperature. Utilizing the formulation of Thermo Field Dynamics (TFD), we can show that Itoʼs stochastic equations for tilde and non-tilde particle positions reproduce the TFD-type Schrödinger equation which is equivalent to the Liouville–von Neumann equation. In our formalism, the drift terms in the Itoʼs stochastic equation have the temperature dependence and the thermal fluctuation is induced through the correlation of the non-tilde and tilde particles. We show that our formalism satisfies the position–momentum uncertainty relation at finite temperature.
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