Extension of Nelsonʼs stochastic quantization to finite temperature using thermo field dynamics

► Utilizing TFD, we extend Nelsonʼs stochastic method to finite temperature. ► We introduce stochastic equations for tilde and non-tilde particles. ► Our stochastic equations can reproduce the TFD-type Schrödinger equation. ► Our formalism satisfies the uncertainly relation at finite temperature.