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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