Related papers: Irreversibility in a simple reversible model
Time reversal symmetric triangular maps of the unit square are introduced with the property that the time evolution of one of their two variables is determined by a piecewise expanding map of the unit interval. We study their statistical…
A new discrete time-reversible map of a unit square onto itself is proposed. The map comprises of piecewise linear two-dimensional operations, and is able to represent the macroscopic features of both equilibrium and nonequilibrium…
The arrow of time is an irreversible phenomenon for a system of particles undergoing reversible dynamics. Since the time of Boltzmann to this day, the arrow of time has led to debate and research. However, the enormous growth of…
Microphysical laws are time reversible, but macrophysics, chemistry and biology are not. This chapter explores how this asymmetry (a classic example of a broken symmetry) arises due to the cosmological context, where a non-local Direction…
Why does time appear to pass irreversibly? To investigate, we introduce a class of partitioned cellular automata (PCAs) whose cellwise evolution is based on the chaotic baker's map. After imposing a suitable initial condition and…
The fundamental time-reversal invariance of dynamical systems can be broken in various ways. One way is based on the presence of resonances and their interactions giving rise to unstable dynamical systems, leading to well-defined time…
We study time-reversal symmetry in dynamical systems with finite phase space, with applications to birational maps reduced over finite fields. For a polynomial automorphism with a single family of reversing symmetries, a universal (i.e.,…
One observes that a considerable level of confusion remains about some of those aspects of irreversibility, entropy generation and `the arrow of time' which actually are well understood. This demands that great care must be taken in any…
Time irreversibility, defined as the lack of invariance of the statistical properties of a system or time series under the operation of time reversal, has received an increasing attention during the last decades, thanks to the information…
We provide a dynamical proof of the second law of thermodynamics, along the lines of an argument of Penrose and Gibbs, making crucial use of the upper semicontinuity of the mean entropy proved by Robinson and Ruelle and Lanford and…
This paper presents a unified formulation of the origin of the arrow of time in classical and quantum mechanics. We begin with a mechanical analysis of a one-dimensional three-particle system, which provides a concrete example in which…
A dynamical system is said to be reversible if, given an output, the input can always be recovered in a well-posed manner. Nevertheless, we argue that reversible systems that have a time-reversal symmetry, such as the Nonlinear…
We study dynamics and bifurcations of two-dimensional reversible maps having non-transversal heteroclinic cycles containing symmetric saddle periodic points. We consider one-parameter families of reversible maps unfolding generally the…
Deriving an arrow of time from time-reversal symmetric microscopic dynamics is a fundamental open problem in many areas of physics, ranging from cosmology, to particle physics, to thermodynamics and statistical mechanics. Here we focus on…
The second law of thermodynamics - the usual statement of the arrow of time - has been called the most fundamental law of physics. It is thus difficult to conceive that a single dynamical system could contain subsystems, in significant…
The issue of irreversibility in a universe with time-reversal-symmetric laws is a central problem in physics. % , and, in particular, to statistical mechanics, information theory and quantum thermodynamics. In this letter, we discuss for…
A broken time-reversal symmetry, i.e. broken detailed balance, is central to non-equilibrium physics and is a prerequisite for life. However, it turns out to be quite challenging to unambiguously define and quantify time-reversal symmetry…
Living systems are fundamentally irreversible, breaking detailed balance and establishing an arrow of time. But how does the evident arrow of time for a whole system arise from the interactions among its multiple elements? We show that the…
In the first half of the paper, some recent advances in coupled dynamical systems, in particular, a globally coupled map are surveyed. First, dominance of Milnor attractors in partially ordered phase is demonstrated. Second, chaotic…
Time-reversibility measured by the deviation of the perturbed time-reversed motion from the unperturbed one is examined for normal quantum diffusion exhibited by four classes of quantum maps with contrastive physical nature. Irrespective of…