where 𝑚 is the particle mass, 𝒓 is the position of a particle, 𝑭 𝐵 is the random force driving Brownian motion, 𝑭 𝑡𝑝ℎ is the thermophoretic force, and 𝛾 is the friction coefficient. Here, since the particle is considered spherical, the friction coefficient is equivalent to drag coefficient obtained from Stokes' law, which is given by 𝛾 = 6𝜋𝜇𝑎 , where 𝜇 is the fluid viscosity and 𝑎 is the particle radius. In this simulation, the viscosity 𝜇 at each temperature was obtained using the approximation 𝜇 = 2.761exp (1713 𝑇 ⁄ ) [Pa s]. Furthermore, since the Reynolds number in the system is sufficiently small (e.g. with kinematic viscosity 𝜈 = 1.0 × 10 -6 [m 2 s -1 ], particle diameter 𝑑 = 0.5 [µm], and characteristic velocity 𝑣 ≪ 1 [m s ], it follows that 𝑅𝑒 = 𝑣𝑑/𝜈 ≪ 1) and the relaxation time of particle is much shorter than the characteristic time scale (e.g., the frame interval of data acquisition in experiments), the system is overdamped, and Equation (3) can be rewritten as follows