Related papers: Time-Irreversibility is Hidden Within Newtonian Me…
We present an algorithm for marginalising changepoints in time-series models that assume a fixed number of unknown changepoints. Our algorithm is differentiable with respect to its inputs, which are the values of latent random variables…
There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time-reversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations…
Finite unit norm tight frames provide Parseval-like decompositions of vectors in terms of redundant components of equal weight. They are known to be exceptionally robust against additive noise and erasures, and as such, have great potential…
Molecular Dynamics and Statistical Mechanics make possible a particle-based understanding of Thermodynamics and Hydrodynamics, including the fascinating Loschmidt contradiction between time-reversible atomistic mechanics and the…
The arrow of time can be quantified through the Kullback-Leibler divergence ($D_{KL}$) between the distributions of forward and reverse trajectories in a system. Many approaches to estimate this rely on specific models, but the use of…
We present an algorithm for the rapid numerical integration of smooth, time-periodic differential equations with small nonlinearity, particularly suited to problems with small dissipation. The emphasis is on speed without compromising…
Reversible algorithms play a crucial role both in classical and quantum computation. While for a classical bit the only nontrivial reversible operation is the bit-flip, nature is far more versatile in what it allows to do to a quantum bit.…
Using molecular dynamics simulations, we show that an asymmetrically shaped nanoparticle in dilute solution possesses a spontaneously curved trajectory within finite time interval, instead of the generally expected random walk. This…
We relate progress in statistical mechanics, both at and far from equilibrium, to advances in the theory of dynamical systems. We consider computer simulations of time-reversible deterministic chaos in small systems with three- and…
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…
Events in the world may be caused by other, unobserved events. We consider sequences of events in continuous time. Given a probability model of complete sequences, we propose particle smoothing---a form of sequential importance…
The dynamics of dissipative soft-sphere gases obeys Newton's equation of motion which are commonly solved numerically by (force-based) Molecular Dynamics schemes. With the assumption of instantaneous, pairwise collisions, the simulation can…
Framing computation as the transformation of metastable memories, we explore its fundamental thermodynamic limits. The true power of information follows from a novel decomposition of nonequilibrium free energy derived here, which provides a…
In non relativistic quantum mechanics time enters as a parameter in the Schroedinger equation. However, there are various situations where the need arises to view time as a dynamical variable. In this paper we consider the dynamical role of…
The mechanism of irreversible dynamics in the systems with mixing is analyzed. The procedure of splitting of system on equilibrium subsystems and studying of dynamics of one of them under condition of its interaction with other subsystems…
Modelling incompressible ideal fluids as a finite collection of vortex filaments is important in physics (super-fluidity, models for the onset of turbulence) as well as for numerical algorithms used in computer graphics for the real time…
Anticipating a tipping point, a transition from one stable steady state to another, is a problem of broad relevance due to the ubiquity of the phenomenon in diverse fields. The steady-state nature of the dynamics about a tipping point makes…
Irreversibility is commonly quantified by entropy production. An external observer can estimate it through measuring an observable that is antisymmetric under time-reversal like a current. We introduce a general framework that, inter alia,…
It has been argued by Grigoriev and Rubakov that one can simulate real time processes involving baryon number non-conservation at high temperature using real time evolution of classical equations, and summing over initial conditions with a…
The inference of thermodynamic quantities from the description of an only partially accessible physical system is a central challenge in stochastic thermodynamics. A common approach is coarse-graining, which maps the dynamics of such a…