Related papers: Irreversibility in a simple reversible model
We consider a class of models describing the dynamics of $N$ Boolean variables, where the time evolution of each depends on the values of $K$ of the other variables. Previous work has considered models with dissipative dynamics. Here we…
Planar polynomial automorphisms are polynomial maps of the plane whose inverse is also a polynomial map. A map is reversible if it is conjugate to its inverse. Here we obtain a normal form for automorphisms that are reversible by an…
A proposal is made for a mathematically unambiguous treatment of evolution in the presence of closed timelike curves. In constrast to other proposals for handling the naively nonunitary evolution that is often present in such situations,…
While routinely used in other areas of dynamics, image sets are ill-defined objects in general non-invertible measurable dynamics. We propose a way of consistently working with image sets of null-preserving (and hence, in particular, of…
A family of discontinuous symplectic maps on the cylinder is considered. This family arises naturally in the study of nonsmooth Hamiltonian dynamics and in switched Hamiltonian systems. The transformation depends on two parameters and is a…
In this paper we consider a one dimensional liner piecewise-smooth discontinuous map. It is well known that stable periodic orbits exist in this type of map for a specific parameter region. It is also known that the corresponding…
Time irreversibility is a common signature of nonlinear processes, and a fundamental property of non-equilibrium systems driven by non-conservative forces. A time series is said to be reversible if its statistical properties are invariant…
The transition probability for time-dependent unitary evolution is invariant under the reversal of protocols just as in the classical Liouvillian dynamics. In this article, we generalize the expression of microscopic reversibility to…
We explore the existence of irreducible and reducible arc-sections in an irreducible hypersurface singularity germ along finite projections. In particular we provide examples of irreducible isolated hypersurface singularities for which no…
The dynamics of time-reversible systems are statistically indistinguishable when observed forward or backward in time. A rich literature of statistical methods to distinguish irreversible dynamics from the reversible dynamics of linear,…
We consider how to tell the time-ordering associated with measurement data from quantum experiments at two times and any number of qubits. We define an arrow of time inference problem. We consider conditions on the initial and final states…
The 2nd law of thermodynamics yields an irreversible increase in entropy until thermal equilibrium is achieved. This irreversible increase is often assumed to require large and complex systems to emerge from the reversible microscopic laws…
We study dynamics of a generic quadratic diffeomorphism, a 3D generalization of the planar H\'{e}non map. Focusing on the dissipative, orientation preserving case, we give a comprehensive parameter study of codimension-one and two…
How does the arrow of time (dissipative, irreversible behavior) emerge from time-reversible Hamiltonian mechanics? Two ingredients are needed: the underlying system must be ergodic or phase-mixing, and our knowledge of the system must be…
An algorithm is described for the construction of actions for scalar, spinor, and vector gauge fields that remains well-defined when the metric is degenerate and that involve no contravariant tensor fields. These actions produce the…
Driven by the term "the arrow of time" as a general topic, the article develops a musical discussion by referring to the etymological origin of the term: philosophy (epistemology) and physics (thermodynamics). In particular, the article…
In this work we define the generalized $\varphi$-pullback attractors for evolution processes in complete metric spaces, which are compact and positively invariant families, such that they pullback attract bounded sets with a rate determined…
Experimental measurements of physical systems often have a limited number of independent channels, causing essential dynamical variables to remain unobserved. However, many popular methods for unsupervised inference of latent dynamics from…
We study evolution algebras of arbitrary dimension. We analyze in deep the notions of evolution subalgebras, ideals and non-degeneracy and describe the ideals generated by one element and characterize the simple evolution algebras. We also…
We consider a class of noisy, one-dimensional quantum cellular automata that allow one to shift from unitary dynamics to completely positive maps, and investigate the notion of reversibility in such a setting. To this aim, we associate an…