Related papers: Probabilistic Turing Machine and Landauer Limit
In this study, we establish a connection between timelike and spacelike entanglement entropy. We show that timelike entanglement entropy is closely related to spacelike entanglement entropy and its temporal derivative. For a broad class of…
Analog quantum simulation is emerging as a powerful tool for uncovering classically unreachable physics such as many-body real-time dynamics. A complete quantification of uncertainties is necessary in order to make precise predictions using…
This note is about encoding Turing machines into the lambda-calculus.
We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…
Decaying states can be represented by Gamow vectors with an exponential, asymmetric time evolution. This asymmetric evolution is a manifestation of irreversibility on the microphysical level. The Rigged Hilbert Space provides a mathematical…
We have studied the nucleation in the two dimensional Ising model by Monte Carlo simulation. The nucleation time has been studied as a function of the magnetic field for various system sizes. The logarithm of the nucleation time is found to…
It is demonstrated how to construct a Galois connection between two related systems with entropy. The construction, called the Landauer's connection, describes coupling between two systems with entropy. It is straightforward and transfers…
Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…
The discussion is limited to first-class parametrized systems, where the definition of time evolution and observables is not trivial, and to finite dimensional systems in order that technicalities do not obscure the conceptual framework.…
We briefly address Landauer's Principle and some related issues in thermal demons. We show that an error-free Turing computer works in the zero-entropy limit, which proves Landauer's derivation incorrect. To have a physical logic gate,…
The dynamics of the spins in the Ising model are analyzed using a virtual walk scenario. The system is quenched from a very high temperature to a lower one using the Glauber scheme in one and two dimensions. A walk is associated with each…
Isoperimetric inequalities form a very intuitive yet powerful characterization of the connectedness of a state space, that has proven successful in obtaining convergence bounds. Since the seventies they form an essential tool in…
This paper demonstrates the relativity of Computability and Nondeterministic; the nondeterministic is just Turing's undecidable Decision rather than the Nondeterministic Polynomial time. Based on analysis about TM, UM, DTM, NTM, Turing…
We consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints. The joint distributions of surface height at finitely many points at a fixed time moment are given as marginals of a…
In CSL'99 Roversi pointed out that the Turing machine encoding of Girard's seminal paper "Light Linear Logic" has a flaw. Moreover he presented a working version of the encoding in Light Affine Logic, but not in Light Linear Logic. In this…
A general nonequilibrium thermodynamic theory is developed for time-dependent Langevin dynamics, starting from the common definition of nonequilibrium Gibbs entropy. It is shown that the notations appearing in the First and the Second Law…
In \cite{Ch91a} it was shown that the billiard ball map for the periodic Lorentz gas has infinite topological entropy. In this article we study the set of points with infinite Lyapunov exponents. Using the cell structure developed in…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…
Overdamped stochastic systems maintained far from equilibrium can display sustained oscillations with fluctuations that decrease with the system size. The correlation time of such noisy limit cycles expressed in units of the cycle period is…
We construct a parallel stochastic dynamics with invariant measure converging to the Gibbs measure of the low temperature Ising model. The proof of such convergence requires a polymer expansion based on suitably defined Peierls-type…