Information transport in classical statistical systems

@article{Wetterich2016InformationTI,
  title={Information transport in classical statistical systems},
  author={C. Wetterich},
  journal={arXiv: Statistical Mechanics},
  year={2016}
}
  • C. Wetterich
  • Published 15 November 2016
  • Physics, Mathematics
  • arXiv: Statistical Mechanics
For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the boundary to the bulk by classical wave functions. The dependence of wave functions on the location of hypersurfaces in the bulk is governed by a linear evolution equation that can be viewed as a generalized Schr\"odinger equation. Classical wave functions obey… 
Quantum formalism for classical statistics
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer
Fermionic quantum field theories as probabilistic cellular automata
A class of fermionic quantum field theories with interactions can be described equivalently as probabilistic cellular automata, namely cellular automata with a probability distribution for the
Quantum computing with classical bits
TLDR
A general formalism for probabilistic computing for which deterministic computing and quantum computing are special limiting cases is proposed, and it is suggested that features of quantum computation or more general Probabilistic computation may be realized by neural networks, neuromorphic computing or perhaps even the brain.
Quantum fermions from classical bits
  • C. Wetterich
  • Physics, Medicine
    Philosophical Transactions of the Royal Society A
  • 2021
TLDR
A simple probabilistic cellular automaton is shown to be equivalent to a relativistic fermionic quantum field theory with interactions, equivalent to the classical statistical system of a generalized Ising model.
The probabilistic world
TLDR
This work discusses entangled quantum systems in terms of classical probability distributions, in which quantum field theories have to be described by an overall probability distribution for the whole Universe for all times.
Ontological states and dynamics of discrete (pre-)quantum systems
The notion of ontological states is introduced here with reference to the Cellular Automaton Interpretation of Quantum Mechanics proposed by G.'t Hooft. A class of discrete deterministic
Qubit exchange interactions from permutations of classical bits
In order to prepare for the introduction of dynamical many-body and, eventually, field theoretical models, we show here that quantum mechanical exchange interactions in a three-spin chain can emerge
A Baker–Campbell–Hausdorff formula for the logarithm of permutations
The dynamics-from-permutations of classical Ising spins is studied for a chain of four spins. We obtain the Hamiltonian operator which is equivalent to the unitary permutation matrix that encodes
Are Quantum Spins but Small Perturbations of Ontological Ising Spins?
  • H. Elze
  • Physics, Mathematics
    Foundations of Physics
  • 2020
The dynamics-from-permutations of classical Ising spins is generalized here for an arbitrarily long chain. This serves as an ontological model with discrete dynamics generated by pairwise exchange
Probabilistic cellular automata for interacting fermionic quantum field theories
A particular version of the Thirring model with imaginary coupling can be represented as a cellular automaton. This interacting fermionic quantum field theory obeys a unitary time evolution and shows

References

SHOWING 1-10 OF 47 REFERENCES
Quantum formalism for classical statistics
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer
Quantum field theory from classical statistics
An Ising-type classical statistical model is shown to describe quantum fermions. For a suitable time-evolution law for the probability distribution of the Ising-spins our model describes a quantum
The emergence of classical properties through interaction with the environment
The dependence of macroscopic systems upon their environment is studied under the assumption that quantum theory is universally valid. In particular scattering of photons and molecules turns out to
Quantum mechanics from classical statistics
Abstract Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states.
Probabilistic Time
The concept of time emerges as an ordering structure in a classical statistical ensemble. Probability distributions pτ(t) at a given time t obtain by integrating out the past and future. We discuss
Emergence of quantum mechanics from classical statistics
The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical
Quantum particles from classical statistics
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being “classical” or “quantum” ceases to be a basic conceptual
Space-Time Approach to Non-Relativistic Quantum Mechanics
Non-relativistic quantum mechanics is formulated here in a different way. It is, however, mathematically equivalent to the familiar formulation. In quantum mechanics the probability of an event which
Gating classical information flow through spin chains by quantum phase transitions
To push commercial electronics beyond its current size limits, atomic-scale communication channels and logic units need to be designed, making the use of quantum entities an imperative. In this
Decoherence, einselection, and the quantum origins of the classical
as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus
...
1
2
3
4
5
...