We think of all dynamical situations as consisting of a space of states and a set of laws codifying how these states are weaved across time, and refer to the actual manifestation of these laws as processes.

Of course, one can argue whether it is sensical to split the reality into states and processes but so far it has been very fruitful to do so.

1. Interchangeability

1.1. Simplicity as Interchangeability of States and Processes

In mathematics, structures (i.e. persisting states) tend to be exactly whatever are preserved by transformations (i.e. processes). That is why Category Theory works, why you can study processes in lieu of states without losing information. (Think of continuous maps vs topological spaces) State and process centric perspectives each have their own practical benefits, but they are completely interchangeable in the sense that both Set Theory (state centric perspective) and Category Theory (process centric perspective) can be taken as the foundation of all of mathematics.

Physics is similar to mathematics. Studying laws is basically the same thing as studying properties. Properties are whatever are preserved by laws and can also be seen as whatever give rise to laws. (Think of electric charge vs electrodynamics) This observation may sound deep, but (as with any deep observation) is actually tautologous since we can study only what does not change through time and only what does not change through time allows us to study time itself. (Study of time is equivalent to study of laws.)

Couple of side-notes:

There are no intrinsic (as opposed to extrinsic) properties in physics since physics is an experimental subject and all experiments involve an interaction. (Even mass is an extrinsic property, manifesting itself only dynamically.) Now here is the question that gets to the heart of the above discussion: If there exists only extrinsic properties and nothing else, then what holds these properties? Nothing! This is basically the essence of Radical Ontic Structural Realism and exactly why states and processes are interchangeable in physics. There is no scaffolding.
You probably heard about the vast efforts and resources being poured into the validation of certain conjectural particles. Gauge theory tells us that the search for new particles is basically the same thing as the search for new symmetries which are of course nothing but processes.
Choi–Jamiołkowski isomorphism helps us translate between quantum states and quantum processes.

Long story short, at the foundational level, states and processes are two sides of the same coin.

1.2. Complexity as Non-Interchangeability of States and Processes

You understand that you are facing complexity exactly when you end up having to study the states themselves along with the processes. In other words, in complex subjects, the interchangeability of state and process centric perspectives start to no longer make any practical sense. (That is why stating a problem in the right manner matters a lot in complex subjects. Right statement is half the solution.)

For instance, in biology, bioinformatics studies states and computational biology studies processes. (Beware that the nomenclature in biology literature has not stabilized yet.) Similarly, in computer science, study of databases (i.e. states) and programs (i.e. processes) are completely different subjects. (You can view programs themselves as databases and study how to generate new programs out of programs. But then you are simply operating in one higher dimension. Philosophy does not change.)

There is actually a deep relation between biology and computer science (similar to the one between physics and mathematics) which was discussed in an older blog post.

2. Persistence

The search for signs of persistence can be seen as the fundamental goal of science. There are two extreme views in metaphysics on this subject:

Heraclitus says that the only thing that persists is change. (i.e. Time is real, space is not.)
Parmenides says that change is illusionary and that there is just one absolute static unity. (i.e. Space is real, time is not.)

The duality of these points of views were most eloquently pointed out by the physicist John Wheeler, who said "Explain time? Not without explaining existence. Explain existence? Not without explaining time".

Persistences are very important because they generate other persistencies. In other words, they are the building blocks of our reality. For instance, states in biology are complex simply because biology strives to resist change by building persistence upon persistence.

2.1. Invariances as State-Persistences

From a state perspective, the basic building blocks are invariances, namely whatever that do not change across processes.

Study of change involves an initial stage where we give names to substates. Then we observe how these substates change with respect to time. If a substate changes to the point where it no longer fits the definition of being A, we say that substate (i.e. object) A failed to survive. In this sense, study of survival is a subset of study of change. The only reason why they are not the same thing is because our definitions themselves are often imprecise. (From one moment to the next, we say that the river has survived although its constituents have changed etc.)

Of course, the ambiguity here is on purpose. Otherwise without any definiens, you do not have an academic field to speak of. In physics for instance, the definitions are extremely precise, and the study of survival and the study of change completely overlap. In a complex subject like biology, states are so rich that the definitions have to be ambiguous. (You can only simulate the biological states in a formal language, not state a particular biological state. Hence the reason why computer science is a better fit for biology than mathematics.)

2.2. Cycles as Process-Persistences

Processes become state-like when they enter into cyclic behavior. That is why recurrence is so prevalent in science, especially in biology.

As an anticipatory affair, biology prefers regularities and predictabilities. Cycles are very reliable in this sense: They can be built on top of each other, and harnessed to record information about the past and to carry information to the future. (Even behaviorally we exploit this fact: It is easier to construct new habits by attaching them to old habits.) Life, in its essence, is just a perpetuation of a network of interacting ecological and chemical cycles, all of which can be traced back to the grand astronomical cycles.

Prior studies have reported that 15% of expressed genes show a circadian expression pattern in association with a specific function. A series of experimental and computational studies of gene expression in various murine tissues has led us to a different conclusion. By applying a new analysis strategy and a number of alternative algorithms, we identify baseline oscillation in almost 100% of all genes. While the phase and amplitude of oscillation vary between different tissues, circadian oscillation remains a fundamental property of every gene. Reanalysis of previously published data also reveals a greater number of oscillating genes than was previously reported. This suggests that circadian oscillation is a universal property of all mammalian genes, although phase and amplitude of oscillation are tissue-specific and remain associated with a gene’s function. (Source)

A cyclic process traces out what is called an orbital which are like invariances that are smeared across time. An invariance is a substate preserved by a process, namely a portion of a state that is mapped identically to itself. An orbital too is mapped to itself by the cyclic process, but it is not identically done so. (Each orbital point moves forward in time to another orbital point and eventually ends up at its initial position.) Hence orbitals and process-persistency can be viewed respectively as generalizations of invariances and state-persistency.

3. Information

In practice, we do not have perfect knowledge of the states nor the processes. Since we can not move both feet at the same time, in our quest to understand nature, we assume that we have perfect knowledge of either the states or the processes.

Assumption: Perfect knowledge of all the actual processes but imperfect knowledge of the state
Goal: Dissect the state into explainable and unexplainable parts
Expectation: State is expected to be partially unexplainable due to experimental constraints on measuring states.
Assumption: Perfect knowledge of a state but no knowledge of the actual processes
Goal: Find the actual (minimal) process that generated the state from the library of all possible processes.
Expectation: State is expected to be completely explainable due to perfect knowledge about the state and the unbounded freedom in finding the generating process.

The reason why I highlighted expectations here is because it is quite interesting how our psychological stance against the unexplainable (which is almost always - in our typical dismissive tone - referred to as noise) differs in each case.

In the presence of perfect knowledge about the processes, we interpret the noisy parts of states as absence of information.
In the absence of perfect knowledge about the processes, we interpret the noisy parts of states as presence of information.

The flip side of the above statements is that, in our quest to understand nature, we use the word information in two opposite senses.

Information is what is explainable.
Information is what is inexplainable.

3.1 Information as the Explainable

In this case, noise is the ideal left-over product after everything else is explained away, and is considered normal and expected. (We even gave the name “normal” to the most commonly encountered noise distribution.)

This point of view is statistical and is best exemplified by the field of statistical mechanics where massive micro-degrees freedom can be safely ignored due to their random nature and canned into highly regular noise distributions.

3.2. Information as the Inexplainable

In this case, noise is the only thing that can not be compressed further or explained away. It is surprising and unnerving. In computer speak, one would say “It is not a bug, it is a feature.”

This point of view is algorithmic and is best exemplified by the field of algorithmic complexity which looks at the notion of complexity from a process centric perspective.