Multi-Dimensional and Dissipative Dynamical Systems: Maximum Entropy as a Principle for Modeling Dynamics and Emergent Phenomena in Complex Systems

Project: Research project

Project Details


Thermodynamic theory led to a fundamental understanding of complex systems operating at equilibrium that fueled the industrial revolution. By contrast, a general framework for modeling complex non-equilibrium systems is lacking despite the broad impact such a framework could have across the biological and material world. For this reason, a collection of phenomenological approaches are currently used to study complex dynamical systems such as motors operating far from equilibrium, biological architectures responsible for signal relays in living cells, and other emergent dynamical phenomena in complex systems.

To build a mathematical framework that can achieve for non-equilibrium systems what thermodynamics has accomplished for systems at equilibrium, a new principle is needed. At the basis of thermodynamics lies the principle of Maximum Entropy (MaxEnt) which is equally
applicable to equilibrium as it is to non-equilibrium systems.

Methods: We propose to extend the general principle of MaxEnt to build data-driven models. Our work is theoretical and numerical. We will benchmark our theoretical results by generating synthetic data. Our goal to develop principled models that will help us control and optimize complex dynamical systems will be achieved through two main objectives:

Objective 1: We will adapt the inverse framework of MaxEnt to infer the dynamics and properties of multi-dimensional non-equilibrium systems. Within the first two years ofthe proposed project, we will build a general framework to infer dynamical laws for nonequilibrium systems directly from the data. This is relevant to predicting the response of material systems to the types of shocks (thermal and mechanical) experienced in combat. We will then explore how our new framework can help improve the efficiency of nanomotors operating far from equilibrium. Significance: Despite operating in noisy environments and being susceptible to strong thermal fluctuations, nanomotors in living cells show high efficiencies. Understanding what controls the magnitude of these efficiencies will help elucidate key optimization principles necessary in mimicking and improving upon architectures found in nature as well as miniaturizing unmanned devices.
Objective 2: We will use MaxEnt to provide a mechanistic understanding of emergent phenomena in multi-dimensional non-equilibrium systems. In the last year and a half, we will focus our attention on the phenomenon of anomalous diffusion routinely encountered across complex systems and show how the principle of MaxEnt can generate mechanistic explanations of anomalous behavior (such as finding spatially-varying forces from the data). We will then describe strategies for controlling the diffusion process once its origins have been
determined. Significance: Understanding anomalous diffusion is relevant to modeling and controlling flow of contaminants in heterogeneous environments, flow through fractured materials, diffusion of viruses in living cells and even the spread of harmful bacteria in a population.
Thus a clear framework for modeling complex dynamical systems would be immediately relevant to fabricating resilient materials, building miniaturized devices and efficient engines as well as developing strategies for stemming the diffusion of viruses in living cells. This would further the Armys mission of protecting soldiers in the field as well as U.S. civilians while critically advancing its technological capability.
Effective start/end date4/15/1710/14/19


  • DOD-ARMY: Army Materiel Command (AMC): $300,000.00

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