Dear Colleagues,

Currently, a silent revolution is taking place in physics and engineering: memory, a long-neglected subject in the “physical sciences”, often more at home in the cognitive and social sciences, is now becoming a fundamental key theme of some of the most innovative and advanced developments in both fundamental mathematical and physical research on one side, and engineering and technology on the other. At its core, memory and memory-retrieval processes are closely connected with symmetric invariance and symmetry breaking. In an abstract manner, a fundamental structure underlying a memory system experiences a structural change that breaks its original symmetric properties; however, the system can still provide a mechanism to recover the original invariance properties in order to retrieve memories now stored through such symmetry-breaking processes.

Examples of memory processes in nature include the move in quantum dynamics from the nearly universal emphasis on Markovianity in the last five or six decades to full explorations of non-Markovian physics where, in the latter case, strong and rapid interactions between the system under observation and its surrounding environments are essential for maintaining long-term correlations and coherence in complex dynamical structures. In computer engineering, we find that neuromorphic computing, especially with the reemerging spiking neural network paradigm, is now becoming one of the most promising hardware/software co-design approaches for future artificial intelligence and machine learning. In circuits and systems, pure memory-like passive or quasi-passive circuit elements, such as mem-resistors, are now being sought and investigated both theoretically and experimentally. In biology, quantum brain dynamics, quantum biology, and classical neuroscience, while adopting radically different perspectives, all agree on the crucial importance of memory mechanisms in biological tissues. In all such areas, the flow of information from the system to the environment is counteracted by opposite processes that sustain memory traces and storage mechanisms. It appears that, whether in computing or in fundamental physics, memory effects are here to stay.

We believe that the time is now ripe for gathering in one place fundamental and key researchers who endeavour to discover how memory, nonlocality, and storage processes are interlinked with one another. Our emphasis will be on structure and function, with physics and mathematics being more closely related to the purely structural aspects of memory (e.g., via nonlocality and non-Markovianity), while function is more visible in biological and engineering contexts (e.g., neuroscience, quantum biology, quantum brain dynamics, neuromorphic computing, and memory circuit elements).

This Special Issue will be the first comprehensive forum for sharing the latest theoretical, computational, and experimental progress made in the general problem of how information, energy, and other physical quantities can be stored, manipulated, and recalled in complex physical systems. The Issue is intentionally designed to be multidisciplinary in scope (and hopefully in content), with contributions invited from participants working in diverse and different areas in physics, mathematics, chemistry, and biology, e.g., quantum physics, quantum engineering, neuromorphic computing, circuit theory, neuroscience, quantum biology, cognitive psychology, artificial intelligence, nonlinear dynamical systems, and others.

We are interested, in particular, in several aspects of memory in nature, covering a wide spectrum of possible applications and ideas, including, but not restricted to, the following areas:

• Fundamental theoretical considerations in theoretical physics and mathematical physics, e.g., understanding memory as a symmetry-breaking process.
• The relationship between memory and nonlocality on one hand, and the symmetric and invariant properties of various concepts of space on the other, e.g., phase space, configuration space, Lorentizian spacetime, moduli spaces, and others.
• The fundamental theoretical connection between non-Markovianity, nonlocality, storage, and symmetry.
• Mathematical models and approaches to non-Markovian processes in pure and applied mathematics.
• Non-Markovianity (nonlocality in time) in classical and quantum dynamics.
• Classical vs. quantum memory in information theory.
• The theory of non-Markovian open quantum dynamical systems.
• Memory, nonlocality, and energy storage in dissipative and complex far-from-equilibrium dynamical systems.
• The relationship between order and memory in chemical, biological, and social systems.
• Energy storage and retrieval in natural systems, such as nonlocal media.
• Energy/information storage and retrieval and engineering systems, such as antennas, receivers, and resonators.
• The fundamental role of memory and asynchronous modes of operations in spiking neural network computing systems.
• Neuromorphic computing and memory: theory and applications.
• Mem-resistors in circuits and systems: theory, applications, and experiments.
• Memory in classical neuroscience and the computational approach to brain function.
• Quantum biological models of memory, such as quantum brain dynamics and others.

Contributions coming from physics, mathematics, and biology will be considered, both covering classical and quantum aspects. Moreover, approaches to memory and complexity in the social sciences and economics will be considered if the fundamental structural role of memory, nonlocality, and time is clearly visible.

Prof. Dr. Said Mikki
Guest Editor

Manuscript Submission Information

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• non-Markovian processes
• non-Markovianity
• nonlocality in time
• nonlocality in space
• spatial dispersion
• spatial memory
• energy/momentum storage
• energy localization
• spiking neural networks
• neuromorphic computing
• mem-resistors
• neuroscience
• quantum biology
• quantum brain dynamics