Observability inequality from measurable sets in time for an evolution equation can be obtained in two different settings: first, when $A$ generates an analytic semigroup and $B$ is an admissible observation operator, and second, when $A$ generates a C_0 semigroup and $B$ is

Observability Inequalities from Measurable Sets for Some Abstract Evolution Equations

Relational observables can enhance the understanding of evolution in Hamiltonian-constrained systems, providing a more structured approach to understanding symplectomorphisms.

Relational evolution of observables for Hamiltonian-constrained systems

This paper unifies quantum and classical speed limits on observables in open quantum systems, providing tighter limits on their speed than previously known.

Unifying Quantum and Classical Speed Limits on Observables

Evolution is the most important theory in biology, explaining every biological detail and guiding our understanding of the fossil record.

Science and evolution

The observed dynamic evolution of a system can be described entirely in terms of stationary observables, implying that any closed system such as the Universe is in a stationary state.

Evolution without evolution: Dynamics described by stationary observables

Local reducibility in constrained systems allows for a complete set of perennials, and the relationship between perennials and observables can be identified using the geometry of the phase space.

Time evolution and observables in constrained systems

Experimental evolution with microorganisms reveals strong adaptations in real time, allowing for assessment of ecoevolutionary theories, improvement of industrial traits, and untangling complex phenotypes.

Experimental Design, Population Dynamics, and Diversity in Microbial Experimental Evolution

This paper presents two mathematical models for transitioning quantum observables from non-commutativity to commutativity in the infinite time limit, using Gamow vectors and scattering theory algebraic formalism.

Evolution of quantum observables: from non-commutativity to commutativity

This paper presents a rigorous formalism for describing the evolution of observables in quantum systems of particles in the mean-field scaling limit, offering an alternative description of the kinetic evolution of quantum many-particle systems to kinetic equations.

Quantum Kinetic Evolution of Marginal Observables

Highly degenerate observables can verify the eigenstate thermalization hypothesis, providing potential pathways towards proofs of thermalization.

Eigenstate Thermalization for Degenerate Observables.

Observable parameters in evolutionary dynamic optimization can improve performance by learning the relationship between optimal solutions and observable parameters, predicting new optimal solutions when the environment changes.

Making use of observable parameters in evolutionary dynamic optimization

The relationship between phylogeny and ontogeny is closely linked, with different theories of evolution and development relying on different time scales and verification methods, and no single theory can fully explain all observables.

Conceptions of Biological Evolution and an Approach to Phylogeny-Ontogeny

This paper presents a field-free, non-linear equation of motion for controlling observables in strongly correlated many-body systems, with rigorous constraints determining controllability limits.

Controlling arbitrary observables in correlated many-body systems

Current semi-analytical and chemodynamical models for the Milky Way galaxy reveal strengths and weaknesses in understanding its morphology, dynamics, color, and chemistry.

Galactic Chemical Evolution

Observability in dynamic evolutionary models can be guaranteed for both sexual and asexual populations near an evolutionarily stable state.

Observability in dynamic evolutionary models.

The algebra of pseudo-observables can be used to treat time evolution and transformations, offering minor changes and a deeper insight into the Hermitian transposition.

The Algebra of the Pseudo-Observables III: Transformations and Time Evolution

Gauge invariant observables in general relativity can be measured using GPS technology, providing a straightforward and realistic physical interpretation.

GPS observables in general relativity

In general relativity, observables are not local components of fields, but rather the intertwined concept of frame of reference and gauge transformations.

Observables in General Relativity

These studies suggest that observable evolution can be understood through various frameworks including mathematical models, quantum and classical systems, biological adaptations, and experimental observations.