Physical fermions in the high-energy physics and condensed matter models have antiperiodic boundary conditions in time. The unconventional periodic boundary conditions for fermions in the path integral expression for the Witten index is the origin of the topological character of this object. These boundary conditions reveal themselves in the operator representation of the Witten index as the alternating sign operator, W = Tr ⁡ ⁡ ( − − 1 ) n ^ ^ M ^ ^ t t ′ , where n ^ ^ is the operator of the number of ghosts/fermions and the finite-time stochastic evolution operator (SEO), M ^ ^ t t ′ = e − − ( t − − t ′ ) H ^ ^ , where, H ^ ^ = L ^ ^ − − ∂ ∂ U − − Θ Θ △ △ ^ ^ = [ d ^ ^ , d ¯ ¯ ^ ^ ] , is the infinitesimal SEO with L ^ ^ being the Lie derivative along the subscript vector field, △ △ ^ ^ being the Laplacian, d ^ ^ = χ χ i ∂ ∂ / ∂ ∂ x i being the exterior derivative, which is the operator representative of the topological supersymmetry (TS), and d ¯ ¯ ^ ^ = − − ( i χ χ ¯ ¯ ^ ^ i ) δ δ i j ( ∂ ∂ j U + Θ Θ ( i B ^ ^ j ) ) , where i B ^ ^ j = ∂ ∂ / ∂ ∂ x j and i χ χ ¯ ¯ ^ ^ j = ∂ ∂ / ∂ ∂ χ χ j are bosonic and fermionic momenta, and with square brackets denoting bi-graded commutator, i.e., it is an anticommutator if both operators are fermionic (contain odd total number of χ χ 's and χ χ ¯ ¯ ^ ^ 's) and a commutator otherwise. The exterior derivative and d ¯ ¯ ^ ^ are supercharges. They are nilpotent, e.g., d ^ ^ 2 = 0 , and commutative with the SEO. In other words, Langevin SDEs possess N=2 supersymmetry. The fact that d ¯ ¯ ^ ^ is a supercharge is accidental. For SDEs of arbitrary form, this is not true.