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We revisit the Coulomb blockade of the tunnel junction with conductance much smaller than  e  2 /  ℏ  . We study the junction with capacitance  C , embedded in an Ohmic electromagnetic environment modeled by a series resistance  R  which produces the Nyquist noise. In the semiclassical limit, the Nyquist noise charges the junction by a random charge with a Gaussian distribution. Assuming the Gaussian distribution, we derive analytically the temperature‐dependent junction conductance  G ( T ) valid for temperaturesk  B   T  ≳   (   R  K   /  2  π  R  )    E  cand resistances    R  ≳   R  K    , whereR  K   =  h  /   e   2andE  c   =   e   2    /  2  C    is the single‐electron charging energy. Our analytical result shows the leading dependence    G   (  T  )   ∝   e   −   E  c   /  4   k  B   T, so far believed to exist only if(   R  K   /  π  R  )    E  c   ≪   k  B   T  ≪   E  cand    R  ≫   R  K    . The validity of our result fork  B   T  ≳   (   R  K   /  2  π  R  )    E  cand    R  ≳   R  Kis confirmed by a good agreement with the numerical studies which do not assume the semiclassical limit, and by a reasonable agreement with experimental data for  R  as low as  R  K . Our result also reproduces various asymptotic formulae derived in the past. The factor of 1/4 in the activation energy  E  c /4 is due to the semiclassical Nyquist noise.

Note on the Coulomb blockade of a weak tunnel junction with Nyquist noise: Conductance formula for a broad temperature range