Symbols time derivative ofp 序，=-1h}是r radial part of the momentum operator P(a.a*) P-function projection onto the state path predictability path predicability operator jor(j) probability of the eventj (D)=(D]Hg) probability density function that the particular set D of data is observed when the system is actually in state k p(但H)=Tr(EH）】 conditional probability that one chooses the hypothesis Hi when He is true classical generalized position component charge density Qa,a*=是(alla Q-function Q quantum algebra field of rational numbers r.r rk k-th eigenvalue of a density matrix Bohr's radius =(优，，) three-dimensional position operator R reflection coefficient R(r) radial part of the eigenfunctions ofin speherical coordinates RR' reference frames R reservoir R field of real numbers real part of a complex quantity z RR(B.中.) rotation operator,generator of rotations Ro resolvent of the operator =∑1ACjk risk operator for the j-th hypothesis IR) initial state of the reservoir spin quantum number 8=(6x,y,)=S/h spin vector operator 社=x士1y raising and lowering spin operators action generic quantum system entropy s=(x,5y,) spin observable time time operato eigenket of the time operatorxxv Symbols ˆ p˙x time derivative of pˆx pˆr = −ıh¯ 1 r ∂ ∂r r radial part of the momentum operator P(α, α∗) P-function Pˆj projection onto the state | j or  b j  P path predictability Pˆ path predicability operator ℘j or ℘(j) probability of the event j ℘k (D) = ℘ (D|Hk ) probability density function that the particular set D of data is observed when the system is actually in state k ℘ Hj|Hk  = Tr ρˆk EˆHj  conditional probability that one chooses the hypothesis Hj when Hk is true qk classical generalized position component Q charge density Q(α, α∗) = 1 π α| ˆρ|α Q-function Q quantum algebra Q( field of rational numbers r spherical coordinate r · r scalar product between vectors r and r rk k-th eigenvalue of a density matrix r0 = h¯ 2 me2 Bohr’s radius rˆ = (xˆ, yˆ,zˆ) three-dimensional position operator R reflection coefficient R(r) radial part of the eigenfunctions of ˆlz in speherical coordinates R, R reference frames R reservoir IR field of real numbers (z) = z+z∗ 2 real part of a complex quantity z Rˆ, Rˆ (β, φ, θ) rotation operator, generator of rotations Rˆ Oˆ resolvent of the operator Oˆ Rˆ j = N k=1 ℘A k Cjkρˆk risk operator for the j-th hypothesis | R initial state of the reservoir s spin quantum number sˆ = (sˆx ,sˆy ,sˆz) = Sˆ/h¯ spin vector operator sˆ± = ˆsx ± ısˆy raising and lowering spin operators S action S generic quantum system S entropy Sˆ = (Sˆx , Sˆy , Sˆz) spin observable t time t ˆ time operator |t eigenket of the time operator