System Theory and Physical Systems |
In General
$ System: A relation
S ⊂ X × Y for some two sets X
= ×i ∈ I
Vi (input set) and
Y = ×i ∈ I
Wi (output set).
$ State set and response function: A pair
C, R with R: (C × X) → Y and
(x, y) ∈ S iff there exists c ∈ C such that R(c, x) = y .
* Conditions: Any system has a C and R; A state set can be defined, e.g., by the set of functions
C:= {fC | fc: X → Y, fc ⊂ S} .
$ Composition of systems: Given two systems, S1 ⊂ (X1 × Z21) × (Y1 × Z12) and S2 ⊂ (X2 × Z12) × (Y2 × Z21), the system S = S1∗ S2 ⊂ (X1 × X2) × (Y1 × Y2) is given by
S:= { ((x1, x2), (y1, y2)) | ∃ z1 ∈ Z12, z2 ∈ Z21, such that ((x1, z2), (y1, z1)) ∈ S1, ((x2, z1), (y2, z2)) ∈ S2} .
* Symmetry: Given a group G acting on X × Y, a system S is G-symmetric iff
for all g ∈ G, x ∈ X, y ∈ Y, (gx, gy) ∈ S iff (x, y) ∈ S .
@ References: Smullyan 61;
Mesarović & Takahara 75.
> Online resources:
see Wikipedia page.
Systems in Physics > s.a. classical systems; Emergent
Systems; Isolated Systems; Open Systems;
state of a system.
* Ingredients: A physical
system has a state, including internal and external correlations, and
internal and external interactions.
@ General references: Szabó IJTP(86) [and elementary objects];
Aerts & Pulmannová JMP(06)-a0811 [state property systems];
Lee & Hoban EPTCS(16)-a1606 [information content, communication complexity].
@ Dimensionality of a system:
Wolf & Pérez-García PRL(09)-a0902 [quantum systems, from evolution];
Gallego et al PRL(10)-a1010,
Hendrych et al nPhys(12)-a1111 [tests].
@ In quantum theory: Dugić & Jeknić IJTP(06)qp/05 [and decoherence theory];
Dugić & Jeknić-Dugić IJTP(08)qp/06 [information-theoretic arguments];
Seidewitz FP(11)-a1002 [systems, subsystems, and their interactions];
> s.a. quantum foundations [ontology]; quantum systems.
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