System
Theory and Physical Systems| System
Theory and Physical Systems |
In General
$ System: A relation S 
X × Y for
some two sets X = ×i in I Vi (input
set) and Y = ×i in 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; Mesarovic & Takahara 75.
Systems in Physics > s.a. classical
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.
@ In general: Szabó IJTP(86)
[and elementary objects].
@ In quantum theory: Dugic & Jeknic IJTP(06)qp/05 [and
decoherence theory]; Dugic & Jeknic-Dugic IJTP(08)qp/06 [information-theoretic
arguments]; > s.a. quantum foundations [ontology], quantum
systems.
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29 mar 2008