Functional Pattern Formation in Thermodynamical Systems
Abstract
What thermodynamic effort do open nonlinear systems expend as they spontaneously form complex patterns? Do highly complex organizations require more energy dissipation than simple ones? Or, are macroscopic patterns relatively neutral in terms of total system energy? Are increased fluctuations in entropy production a thermodynamic harbinger of pattern emergence? The answers, surprisingly unavailable at the present, late stage of statistical mechanics and nonlinear dynamics, appears to require a novel synthesis. This project brings together exciting results from three active research areas to address these questions. The first---information thermodynamics---connected recent advances in nonequilbrium thermodynamics with information theory to provide a cutting-edge understanding of Maxwell s Demon. It answers questions such as " Can a Demon extract energy from a thermal bath utilizing control information? How can information be a fuel?" Having come to fruition in the last two decades or so, the second---pattern formation theory---describes the mechanisms that drive spatially-extended systems to spontaneously organize into patterns of activity. It provides techniques that predict how a system dynamically amplifies inherent instability to macroscopic scales, eventually stabilizing emergent patterns via nonlinear attenuation. The third---meromorphic functional calculus--- provides the key new mathematical methods required to analyze the infinite-dimensional hidden linear dynamic of complex spatial patterns and temporal behaviors---patterns and behaviors implicated in both information thermodynamics and pattern formation. Success in the proposed synthesis will impact both our fundamental physical understanding of the energetics guiding far-from-equilibrium pattern formation and our ability to engineer and control emergent patterns that support functional behaviors, such as information processing, computation, and energy conversion. The abiding puzzle is how these systems balance constraint and fluctuation in the service of their functionality. All physical, chemical, and biological systems and all designed technologies are subject to thermodynamic constraints---energy conservation, entropy increase during macroscopic manipulations, and the like . This is especially true and challenging for those whose functioning relies on information processing embodied in emergent patterns. Nanoscale technology most aptly illustrates these fundamental limits. At these scales, we encounter finite-size induced fluctuations that can compromise a device s operation. Even technologies that do not yet depend on quantum effects have rapidly approached limits imposed by microscopic fluctuations. Similar conclusions hold for chemical and biomolecular processes. For example, motor proteins carry-out essential biological functions, such as intracellular nutrient transport, all the while bathed in fluctuations whose energetics fall at the same scale as the ATP-driven motion itself . On the one hand, the increasing demand for computation, combined with the nee d for new computational architectures and substrates, and our increasing ability to control and even design biological processes, on the other, make the proposed synthesis particularly relevant and timely. Understanding the functioning of this wide range of systems turns on developing a new theory of functional pattern formation in thermo-dynamical systems---systems that, at one and the same time, are dynamical systems (behaving and processing and storing information) and are large-scale physical systems (consisting of energetic microscopic subsystems). Our expertise in the above three research areas will bring unique perspectives and insights to this challenge, increasing the likelihood of success.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Sep 11, 2018
- Source ID
- W911NF1810028
Entities
People
- James P. Crutchfield
Organizations
- Army Contracting Command
- United States Army
- University of California, Davis