Two-dimensional visualisation of Shannon entropy

shannonEntropy.m

ShannonEntropy[probs_] := -Total[# * Log @ #] & @ DeleteCases[probs, _?PossibleZeroQ];
par[t_, s_] = {1, 0, 0} + t / Sqrt@2 {-1, 1, 0} + s/Sqrt[3/2] {-1/2, -1/2, 1} // Simplify;
par[pars_List] := par @@ pars;
ContourPlot[
  ShannonEntropy@par[t, s], {t, 0, Sqrt@2}, {s, 0, Sqrt[3/2]}, 
  PlotRange -> All,
  ColorFunction -> "TemperatureMap", PlotRangePadding -> None,
  Contours -> 10,
  FrameStyle -> Directive[Large, Black, FontFamily -> "Latin Modern Math"],
  FrameLabel -> (MaTeX[#, Magnification -> 2] & /@ {"t", "s"}),
  AspectRatio -> Sqrt[3/2]/Sqrt[2]
  ] ~ Show ~ Graphics[{[email protected], Purple,
   Circle[{1/Sqrt@2, 1/Sqrt@6}, 0.4]
  }
]