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We present an extension of Nelson's stochastic quantum mechanics to finitetemperature. Utilizing the formulation of Thermo Field Dynamics (TFD), we canshow that Ito's stochastic equations for tilde and non-tilde particle positionsreproduce the TFD-type Schr\"odinger equation which is equivalent to theLiouville-von Neumann equation. In our formalism, the drift terms in the Ito'sstochastic equation have the temperature dependence and the thermal fluctuationis induced through the correlation of the non-tilde and tilde particles. Weshow that our formalism satisfy the position-momentum uncertainty relation atfinite temperature.

Extension of Nelson's Stochastic Quantization to Finite Temperature Using Thermo Field Dynamics