State of a Physical System |

**In General** > s.a. fluid [equation of state];
phase space; Position
\ physical systems.

* __Idea__: A way to summarize the available
information on a system at an instant, which allows us to predict results of measurements
(associates numbers with observables) and future evolution of the system (using dynamical
equations).

* __Steady state__: A state
in which physical quantities don't depend on time; If the system in question
is isolated, it will also be in equilibrium; If the system is not isolated, there
may be non-zero velocities, flows (stationary vs static, or "non-equilibrium"
vs equilibrium, steady state).

@ __General__: Thirring 81 (v III: 81, 2.2);
Ludwig FP(90);
Folse qp/02-proc [N Bohr's concept];
Giulini in-a1306 [instants in physics];
Scandolo et al a1805
[objectivity, classical states and theories without objective states];
Boughn a1903 [conceptual, and quantum theory].

@ __Covariant notion__: Rovelli gq/01.

**In Classical Theory**
> s.a. poisson structure [structure on the space of states].

* __Idea__: A (time-dependent) measure on phase space;
Possibly δ-function like, a specification of the value of *q* and *p*,
or *q* and *q*^{·}, at a time *t*,
otherwise a statistical distribution function.

@ __References__: Mashburn FP(08) [order model for infinite classical states];
Khanna et al a1112 [state reconstruction].

> __Specific theories__: see states in
statistical mechanics, Macrostates and Microstates.

**In Quantum Theory** > s.a. quantum states
[including space of states] and quantum field theory states.

* __Idea__: A normed, positive
linear functional on the algebra of observables (often a wave function or state
vector in a Hilbert space).

* __Most general__: A map of the form
*a* \(\mapsto\) tr(*ρa*), where *a* is a density matrix.

* __Mohrhoff__: Quantum states
are fundamentally algorithms for computing correlations between possible measurement
outcomes, rather than evolving ontological states
[@ Mohrhoff IJQI(04)qp].

* __And experiments__: Outcomes
of experiments do not correspond to states directly; They indicate properties
of probability distributions for outcomes; Probability distributions leave open
a choice of quantum states and operators and particles, resolvable only by a guess.

@ __General references__: Newton AJP(04)mar;
Madjid & Myers AP(05)
[associating outcomes of experiments to states];
Domenech et al AdP(06)qp [actual and possible properties];
Chovanec & Frič IJTP(10) [states as morphisms];
Bohm & Bryant IJTP(11)-a1011-conf [states vs observables, and asymmetric time evolution];
Khanna et al EJP(12)-a1112 [state reconstruction, tomography vs mutually unbiased bases].

@ __Covariant notion__: Reisenberger & Rovelli PRD(02)gq/01;
> s.a. relativistic quantum mechanics.

> __Related topics__: see observable
algebras; quantum statistical mechanics [including paradox].

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