Related papers: H-theorem do-conjecture
We study the asymptotic properties of the trajectories of a discrete-time random dynamical system in an infinite-dimensional Hilbert space. Under some natural assumptions on the model, we establish a multiplica-tive ergodic theorem with an…
A long and intense debate in philosophy is concerned with the question whether there can be haecceistic differences between possible worlds, that is, nonqualitative differences that only arise from different de re representations. According…
We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady-state by using joint probability distributions symmetries of different entropy production decompositions. The analytical approach is…
The variational method is very important in mathematical and theoretical physics because it allows us to describe the natural systems by physical quantities independently from the frame of reference used. A global and statistical approach…
In low temperature supercooled liquid, below the ideal mode coupling theory transition temperature, hopping and continuous diffusion are seen to coexist. We present a theory which incorporates interaction between the two processes and shows…
Entropy is the distinguishing and most important concept of our efforts to understand and regularize our observations of a very large class of natural phenomena, and yet, it is one of the most contentious concepts of physics. In this…
In the last decade, minimal kinetic models, and primarily the Lattice Boltmann equation, have met with significant success in the simulation of complex hydrodynamic phenomena, ranging from slow flows in grossly irregular geometries to fully…
Mechanics can be founded in a principle stating the uncertainty in the position of an observable particle delta-q as a function of its motion relative to the observer, expressed in a trajectory representation . From this principle,…
Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often…
We examine the conditions under which the thermodynamic behaviour of gravity can be explained within an emergent gravity scenario, where the metric is defined as a composite operator. We show that due to the availability of a boundary of a…
The lattice Boltzmann equation can be viewed as a discretization of the continuous Boltzmann equation. Because of this connection it has long been speculated that lattice Boltzmann algorithms might obey an H-theorem. In this letter we prove…
The recent transition from decelerated to accelerated expansion can be seen as a reflection (or "bounce") in the connection variable, defined by the inverse comoving Hubble length ($b=\dot a$, on-shell). We study the quantum cosmology of…
Contextual equivalence is the de facto standard notion of program equivalence. A key theorem is that contextual equivalence is an equational theory. Making contextual equivalence more intensional, for example taking into account the time…
Are your perceptions, memories and observational data, a statistical fluctuation out of the thermal equilibrium of the universe, having no correlation with the actual past state of the universe? Arguments are given in the literature for and…
It is shown that statistical mechanics is applicable to isolated quantum systems with finite numbers of particles, such as complex atoms, atomic clusters, or quantum dots in solids, where the residual two-body interaction is sufficiently…
Polydisperse systems are commonly encountered when dealing with soft matter in general or any non simple fluid. Yet their treatment within the framework of statistical thermodynamics is a delicate task as the latter has been essentially…
High dimensional random dynamical systems are ubiquitous, including -- but not limited to -- cyber-physical systems, daily return on different stocks of S&P 1500 and velocity profile of interacting particle systems around McKeanVlasov…
Aiming to provide a new class of game dynamics with good long-term rationality properties, we derive a second-order inertial system that builds on the widely studied "heavy ball with friction" optimization method. By exploiting a well-known…
There exists a wide variety of works on the dynamics of large populations ranging from simple heuristic modeling to those based on advanced computer supported methods. Their interconnections, however, remain mostly vague, which…