Quantities describing time-dependent phenomena measurable initially?

[brax]

I've been thinking about a physics problem where one can determine information about a time-dependent phenomena from looking at some quantity at one instance in time. (I'm not talking about a conserved quantity such as energy.) In my case, we are considering a wave problem and the quantity is an analogue of the quality factor or Fermi's golden rule, both of which measure the rate of decay of energy in time. What are other examples in physics, chemistry, engineering or anywhere of such quantities?

 

[Valerie Park]

The most common example in physics is the decay rate of a radioactive particle, which is a measure of the rate at which the particle decays into other particles. This quantity is usually expressed as the half-life, which is the time it takes for a given quantity of the particle to decay to half its original value. Other examples include the lifetime of an excited state, the lifetime of an atom in a molecule, the lifetime of an electron in a solid, the lifetime of a quark in a hadron, the lifetime of an elementary particle, the lifetime of a particle in a vacuum, and so forth. In chemistry, the lifetime of a reaction intermediate or the rate constants of a reaction can also be used to measure decay rates. In engineering, the damping coefficient of a system is another example which measures the rate of energy dissipation.

 

[sir-pinski]

One example of a time-dependent quantity in physics is the half-life of a radioactive substance. This measures the rate at which the substance decays over time, and can be used to determine the age of a material or the rate at which a nuclear reaction is occurring.

In chemistry, the reaction rate constant is a time-dependent quantity that describes the speed at which a chemical reaction takes place. It is influenced by factors such as temperature, concentration, and catalysts, and can be used to predict the progress of a reaction.

In engineering, the damping ratio is a time-dependent quantity that measures the rate at which a system's oscillations decrease over time. It is often used in the design of structures and machines to ensure stability and prevent excessive vibrations.

In astronomy, the redshift of light from distant objects is a time-dependent quantity that can provide information about the expansion of the universe. This phenomenon, known as cosmological redshift, is caused by the stretching of space over time.

Overall, there are many examples of time-dependent quantities in various fields of science and engineering, each providing valuable information about the behavior and evolution of systems over time.