of constituent elements (processing nodes, whether perceptrons or miners, which can be seen as particles) to make high-probability guesses about reality states of the world. Hence, statistical physics could be a good basis for the formalization of smart networks.
Maxwell was among the first to suggest the application of probability as a general model for the study of the science of the very small. Statistical mechanics was likewise intended as a general method based on probability in its early development by Gibbs, following on from classical mechanics (Gibbs, 1902). The aim of statistical mechanics is to address all aspects of mechanical systems, at both the microscopic and macroscopic levels, for example, to explain transitions between gaseous and non-gaseous states.
The thermodynamic aspect of statistical physics is relevant in the formulation of SNFTs because smart networks are physical systems with thermodynamic effects. Blockchains are worldwide physical network systems, comprising about 10,000 nodes on average hosting the transaction ledger for Bitcoin [10,403 (Bitnodes, 2019)] and Ethereum [8,141 (Ethernodes, 2019)]. Deep learning networks too have a physical basis, in that they run on dedicated hardware systems (NVIDIA GPU networks and Google TPU clusters). Concepts such as work, heat, and energy have thermodynamical measures in smart network systems. Blockchains perform work in the form of consensus algorithms (proof-of-work, proof-of-stake, etc.) being a primary mechanism for providing network security and updating the ledger balances of the distributed computing system. Deep learning networks also perform work in the sense of running an operating cycle to derive a predictive classification model for data. The network expounds significant resources to iteratively cycle forward and back through the layers to optimize trial-and-error guesses about the weighting of relevant abstracted feature sets such that new data can be correctly identified.
Technophysics formulations of blockchains and deep learning have been proposed on the basis of thermodynamic properties. For example, a blockchain proof-of-work consensus process could be instantiated as an energy optimization problem with Hamiltonian optimizers and executed as a quantum annealing process on quantum computers (Kalinin & Berloff, 2018). In deep learning, a thermodynamics of machine learning approach is used to propose representation learning as an alternative framework for reasoning in machine learning systems, whose distortion could be measured as a thermodynamical quantity (Alemi & Fischer, 2018).
2.6Field Theory
A field theory is a theory that describes a background space and how the constituent elements in the space behave. In classical physics, a field is a region in which each point is affected by a physical quantity, be it a force, a temperature or any other scalar, vector, or tensor quantity. For example, objects fall to the ground because they are affected by the force of Earth’s gravitational field. A field is a region of space that is affected by a physical quantity that can be represented with a number or a tensor (multi-dimensional number), that has a value for each point in space and time. A weather map, for example, has a temperature assigned to each point on a map. The temperatures may be studied at a fixed point in time (today’s temperature) or over a time interval to understand the dynamics of the system (the effects of temperature change).
Field theories are a particularly good mechanism for studying the dynamics of a system. The dynamics of a system refers to how a system changes with time or with respect to other independent physical variables upon which the system depends. The dynamics are obtained by writing an equation called a Lagrangian or a Hamiltonian of the field, and treating it as a classical or quantum mechanical system, possibly with an infinite number of degrees of freedom (parameters). The resulting field theories are referred to as classical or quantum field theories. The dynamics of a classical field are typically specified by the Lagrangian density in terms of the field components; the dynamics can be obtained by using the action principle. The dynamics of a quantum field are more complicated. However, since quantum mechanics may underlie all physical phenomena, it should be possible to cast a classical field theory in quantum mechanical terms, at least in principle, and this is assumed in the SNFT and SNQFT constructions.
2.6.1 The field is the fundamental building block of reality
At the quantum mechanical scale, the intuition behind field theory is that fields, not particles, may be the fundamental building blocks of reality. For example, Feynman points out that in the modern framework of the quantum theory of fields, even without referring to a test particle, a field occupies space, contains energy, and its presence precludes a classical true vacuum. This has led physicists to consider fields to be physical entities and a foundational aspect of quantum mechanical systems. The fact that the electromagnetic field can possess momentum and energy makes it very real (Feynman, 1970). One resulting interpretation is that fields underlie particles. Particles are produced as waves or excitations of socalled matter fields. Reality may be composed of fluid-like substances (having properties of flow) called fields. Quantum mechanical reality may be made up of fields, not particles.
2.6.2 Field theories: Fundamental or effective
Theories are either fundamental or effective. Fundamental theories are foundational universal truths and effective theories are reasonably effective theories, given the absence of additional proof or knowledge. Fundamental theories have the tony weight of absolute truth. Effective theories serve effectively in the sense of being a reasonable approximation of situations that are not yet fully understood. Classical theories of physics were initially thought to be fundamental, but then found not to be valid everywhere in the universe. Newtonian physics describes pulleys, but not electrons or detailed planetary movement (Einsteinian physics is used in GPS technology). In this sense, all theories of nature are effective theories, in that each is a possible approximation of some more fundamental theory that is as yet unknown.
There is another sense of the meaning of effective field theories, which is that the theory is only effective within a certain range. An effective theory may only be true within certain parameters or regimes, typically whatever domain or length-scale is used to experimentally verify the theory (Williams, 2017). For example, an effective field theory is a way to describe what happens at low energies and long wavelengths (in the domain of general relativity) without having a complete picture of what is happening at higher energies (in the domain of quantum mechanics). In high-energy physics (particle physics), processes can be calculated with the so-called Standard Model without needing to have a complete picture of grand unification or quantum gravity. The opposite is also true, when calculating problems in low-energy physics (gravitational waves), the effects of higher-energy physics (particle physics) can be bracketed out or summed up with a few measurable parameters (Carroll et al., 2014). Each domain has field theories that are effective within its scale-range. The difficulty is deriving field theories that explain situations in which high-energy physics and low-energy physics come together such as black holes.
2.6.2.1Effective field theories in quantum mechanics
Whereas a classical field theory is a theory of classical fields, a quantum field theory is a theory of quantum mechanical fields. A classical field theory is typically specified in conventional space and time (the 3D space and time of Euclidean macroscale reality). On the other hand, a quantum field theory is specified on some kind of background of different models of space and time. To reduce complexity, quantum field theories are most generically placed on either a fixed background such as a flat space, or a Minkowski space (3D quantum mechanical space–time). Whatever space and time region in which the quantum field theory is specified, the idea is to quantize the geometry and the matter contents of the quantum field into an effective theory that can be used to perform calculations. Effective field theories are useful because they can span classical and quantum domains, and more generally, different levels in systems with phase transitions. The SNFT is both a classical field theory and a quantum field theory.
2.6.3 The smart network theories are effective field theories
The
