Information dynamics means how information changes, moves, and stabilizes over time inside a system. Instead of asking what information does the system have, we ask: how does the information evolve? There are various systems where information evolves, like the brain reasoning about a problem or an AI model processing the prompt. Therefore the focus is on the process and not just content.

As we know, traditional information theory, such as Claude Shannon's, mostly studies information transmission, communication channels, and data compression. But it usually treats information as static. Information dynamics asks a different question: What are the laws governing the evolution of information states?

Now we need to consider the idea of information state. Let's define a state, the system's internal information state:

x(t)

This means x is the current configuration of knowledge, beliefs, or representations and t is time. Therefore, the system moves through a space of possible states. This space is called a state space or information manifold.

Now we define how the state evolves. Because dynamics is how the state changes. In continuous-time, we have something like:

dx/dt = F(x, t)

This means the change in the information state depends on some function F. F could represent reasoning processes, learning, internal conflicts, or decision forces. So information dynamics is equal to rules that govern F.

We now lock in on energy landscapes to better understand the systems we design. The idea is that systems try to minimize the energy of the system. Now suppose we define an energy function:

E(x)

This assigns a value to every state. For example, if the energy is high, there is a conflict in the system. If the energy is low, the system is in coherent configuration. Therefore the system can evolve by gradient descent:

dx/dt ​= −∇ E(x)

The state moves downhill on the energy landscape. That means it produces stable states called attractors. Attractors are stable information structures. An attractor is a state where the system stops changing.

Mathematically:

∇ E(x*) = 0

So the system converges to x* and it represents the stable information structure. That means it could be a final interpretation of a problem, a stable belief, or a learned memory pattern.

Now let's overview an example such as reasoning as dynamics. Imagine a system trying to understand a question. At the initial state, there are many competing interpretations. Energy is high because the interpretations disagree. As the system processes information, inconsistent interpretations weaken, coherent ones strenghten. Eventually, the system reaches a stable interpretation. The final interpretation is an attractor of the information dynamics.

It makes our perspective powerful.

We do not treat intelligence as a sequence of rules, our view treats it as a dynamical system evolving in an information landscape. This allows us to study things like stability of reasoning, emergence of decisions, formation of memory structures, or adaptation over time using the mathematics of dynamical systems.

To give you a general mathematical picture, we show a full information-dynamical model that looks like:

dx/dt = −∇ E(x) + G(x,t)

Where E(x) represents internal coherence and G(x,t) represents external inputs or as we call them, forces. The interplay of these determines how the system evolves. Thus you can think of information dynamics such that information is defined by position, reasoning is defined by motion, coherence is defined by gravity, and memory is defined by landscape shape. To simplify this approach to your taste, we say that the system moves through an abstract landscape until it settles into stable structures.

What we showed you was a generic model of how information can be represented. Our work in the Pensive AI Research Division led to our theoretical papers that we published on Zenodo. We also published an introduction on Medium. These papers are:

1. Empathy Energy Minimization in the Reasoning Turing Machine (RTM)

2. Intelligent Action

3. Gödel Memory

These papers are placed in a community that can be accessed through this link:

Information Dynamics of General Intelligence

One day we will get to know each other, but for now, my name is Mehdi Sabzalian.

March 15, 2026

Montreal