### Scientific context and research program

With the discovery of deterministic chaos, it became apparent that even simple interactions between elementary constituents, such as molecules, yield arbitrarily-complex behaviors at large scales. Conversely, observed (or hidden) patterns in empirically measured data can originate either from inherent complexity of constituents at the micro-scale or from the very dynamics of their interactions. However, statistical physics also tells us that complicated elementary interactions (e.g., collisions between gas molecules) can be effectively summarized at large scales with only a few relevant statistical parameters, such as temperature, pressure… In this case, information concerning the relative positions, orientations, and velocities of each molecule is inconsequential at large scale and can be omitted for all practical purposes: configurations with the same global energy level are thermodynamically equivalent.

In this light, the key questions for modeling physical systems become: What are the important objects of study at each description level? How to detect patterns in the first place? To recover the observed patterns and their dynamics, is it possible to formally express (with analytical formula or via a computer program) the interactions between system constituents? Although powerful mathematical tools and conceptual frameworks have been developed over years of research on complex systems and nonlinear dynamics, in the general setting addressed by computational mechanics, these questions are largely unanswered.

Quasi-static and near-equilibrium thermodynamics taught us to describe a system in terms of its global energy. Traditional Hamiltonian mechanics taught us to describe the microscopic evolution of the system in terms of transformations of that energy. And, indeed, thinking in terms of where work is produced and how dissipated energy is transformed brings useful insights to a system’s behavior and organization. For example, detecting work in the motor cortex from EEG signals indicate the execution of some intended action, compared to a rest state. We now realize, however, that most interesting scenarios operate far from thermo-dynamic equilibrium and, in general, that predicting them is not amenable to thermodynamics and statistical physics. Such scenarios, in fact, correspond to steady dynamic states where energy flows in the system and is continuously dissipated to its environment. Such dynamic states, by definition, do not exist at equilibrium.

For example, while a sand pile is static at rest, all its interesting flow patterns, including avalanches, only occur when energy is fed in. Every biological cell lives out of equilibrium, always transforming energy to maintain its structure. Physical patterns, such as vortices in fluid dynamics or granular flows, also occur and persist through time only due to energy dissipation. In these cases, though, what matters most is not so much that energy is dissipated, which is a prerequisite for sustained patterns, but how that energy is dissipated. Does it produces pattern and create information? Does this information persists through time? For example, an electric circuit with capacitors, inductors, and resistors can be built to dissipate the same energy as observed in the example EEG signal above. And, it can be tuned to dissipate that energy at the same time scales (e.g., has the same power spectrum). What matters most, however, is the manner and pathways through which energy is dissipated. And, this differs greatly between the two systems.

One path for describing such systems focuses on how information is produced (emergence of patterns, of large-scale structures) and on how that information is maintained and transformed at different scales. One goal is to search for the analog of Hamiltonian dynamics, but that describes information transformations instead of energy transformations. This would be an equivalent of thermodynamics, but one that operates on states of similar information content instead of on states of similar energy levels. With this, substantial progress would be made towards the physical description and modeling of complex natural phenomena.

Through this collaboration, we aim to address some of these challenging questions, including especially automated detection of patterns and structures at various scales and quantifying and expressing the amount of information they contain. This then will provide a new and novel modeling framework that expresses the ways information is transformed and communicated within complex systems.