情報処理の熱力学2014 5 8 1 Maxwell’s demon [1] 19 [2] 1 1 [3] 2 3 4 5 6 7 8 2 Szilard engine 1 1(a) T (b) 1 ln 2 1(c) (d) kBT ln 2 kB 1929 [4] Brillouin [5] Landauer [6] Bennett [7] 2 2 20 [8] 2 ln BT k 2 ln 1: 21 20 20 3 kBT ln 2 kBT ln 2 3 Shannon information mutual information 4 x x X p[x] ∑ x∈X p[x] = 1 X S(X) := − ∑ x∈X p[x] ln p[x] (1) x x N (< +∞) 0 ≤ S(X) ≤ ln N S(X) = ln N x p[x] = 1/N S(X) = 0 x p[x] =
