I think I changed the notation (sorry!)
A -> S
B -> 1
C -> 2

Here I will consider both the forward process (AB-> AC) and its "time-reversal" (AC -> AB). 
There is a neat fluctuation theorem if we compare both.

LoadSpinChainMatrices[3,"a"];
V1 = g (sp[1].sm[2]+sm[1].sp[2]);
V2 = g(sp[1].sm[3]+sm[1].sp[3]);

ρS = {{1-fS,0},{0,fS}};
ρ1 = {{1-f1,0},{0,f1}};
ρ2 = {{1-f2,0},{0,f2}};
ρ0 = kron[ρS,ρ1,ρ2];

simp={g>0,t>0,0<fS<1,0<f1<1,0<f2<1};
temps = {fS->(1/(Exp[βS ]+1)),f1->(1/(Exp[β1 ]+1)),f2->(1/(Exp[β2 ]+1))};

(* Unitary of the forward process *)
U = MatrixExp[-I V2 t].MatrixExp[-I V1 t];

(* Unitary of the backward process *)
Urev = MatrixExp[-I V1 t].MatrixExp[-I V2 t];

tups = Tuples[{0,1},3]

rep = Thread[Range[1,8]->tups]

(* Computational basis *)
Clear[𝒱]
Do[
𝒱[n/.rep] = Normal@Eye[8][[n]];
,{n,8}];
?𝒱

(* Allowed heat values (in units of Ω = 1) *)
HeatVals = Tuples[{1,0,-1},2]

(* Forward and backward heat distributions *)
Clear[𝒫,𝒫r];
Do[
𝒫[heat] = FullSimplify[
Sum[KroneckerDelta[heat[[1]],(ν1-μ1)] KroneckerDelta[heat[[2]],(ν2-μ2)]
((Abs[𝒱[{m,ν1,ν2}].U.𝒱[{n,μ1,μ2}]])^2) ρS[[n+1,n+1]] ρ1[[μ1+1,μ1+1]] ρ2[[μ2+1,μ2+1]],{n,{0,1}},{m,{0,1}},{μ1,{0,1}},{μ2,{0,1}},{ν1,{0,1}},{ν2,{0,1}}],
simp];

𝒫r[heat] = FullSimplify[
Sum[KroneckerDelta[heat[[1]],(ν1-μ1)] KroneckerDelta[heat[[2]],(ν2-μ2)]
((Abs[𝒱[{m,ν1,ν2}].Urev.𝒱[{n,μ1,μ2}]])^2) ρS[[n+1,n+1]] ρ1[[μ1+1,μ1+1]] ρ2[[μ2+1,μ2+1]],{n,{0,1}},{m,{0,1}},{μ1,{0,1}},{μ2,{0,1}},{ν1,{0,1}},{ν2,{0,1}}],
simp];

,{heat,HeatVals}]

?𝒫

?𝒫r

The fluctuation theorem now reads

((P((Subscript[Q, 1]),(Subscript[Q, 2])))/((Subscript[P, R])(-(Subscript[Q, 1]),-(Subscript[Q, 2])))) = (e^((Subscript[Δβ, 1])(Subscript[Q, 1])+(Subscript[Δβ, 2])(Subscript[Q, 2])))

where (Subscript[Δβ, i]) = (Subscript[β, S]) - (Subscript[β, i])

{Exp[-(βS-β1) h1-(βS-β2)h2],((𝒫[{h1,h2}])/(𝒫r[{-h1,-h2}]))}/.{h1->1,h2->-1}/.temps//Simplify

{Exp[-(βS-β1) h1-(βS-β2)h2],((𝒫[{h1,h2}])/(𝒫r[{-h1,-h2}]))}/.{h1->1,h2->0}/.temps//Simplify

We can also obtain from this a non-equilibirum equality 

⟨(e^(-(Subscript[Δβ, 1])(Subscript[Q, 1])-(Subscript[Δβ, 2])(Subscript[Q, 2])))⟩ = 1

G = Sum[Exp[r1 h1] Exp[r2 h2] 𝒫[{h1,h2}],{h1,{1,0,-1}},{h2,{1,0,-1}}]//Simplify;
G/.temps/.{r1->βS-β1,r2->βS-β2}//Simplify