Related papers: Nonlinear dynamical systems: Time reversibility {\…
The fluctuation relations, which characterize irreversible processes in Nature, are among the most important results in non-equilibrium physics. In short, these relations say that it is exponentially unlikely for us to observe a…
Nonequilibrium thermodynamics of a general second-order stochastic system is investigated. We prove that at steady state, under inversion of velocities, the condition of time-reversibility over the phase space is equivalent to the…
Our goal is to recover time-delayed latent causal variables and identify their relations from measured temporal data. Estimating causally-related latent variables from observations is particularly challenging as the latent variables are not…
The classical theory of linear response applies to statistical mechanics close to equilibrium. Away from equilibrium, one may describe the microscopic time evolution by a general differentiable dynamical system, identify nonequilibrium…
The main goal of the paper is to define and use a condition sufficient to choose a unique solution to conservation law systems with a singular measure in initial data. Different approximations can lead to solutions with different…
It is proven, without using the microscopic reversibility argument of Onsager, that lossy reciprocal systems have a hidden time-reversal symmetry. The key idea is that the dissipation channels of lossy dielectrics can be mimicked by a…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
In this paper, we reveal a general relationship between model simplification and irreversibility based on the model of continuous-time Markov chains with time-scale separation. According to the topological structure of the fast process, we…
Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The…
I compare the role of the information in the classical and quantum dynamics by examining the relation between information flows in measurements and the ability of observers to reverse evolutions. I show that in the Newtonian dynamics…
We describe a way of interpreting the chaotic principle of (ref. [GC1]) more extensively than it was meant in the original works. Mathematically the analysis is based on the dynamical notions of Axiom A and Axiom B and on the notion of…
All presently available results lead to the conclusion that nonextensivity, in the sense of nonextensive statistical mechanics (i.e., $q \ne 1$), does {\it not} modify anything to the second principle of thermodynamics, which therefore…
The time irreversibility problem is the dichotomy of the reversible microscopic dynamics and the irreversible macroscopic physics. This problem was considered by Boltzmann, Poincar\'e, Bogolyubov and many other authors and though some…
A simple deterministic and time reversal invariant type of thermostat is proposed to be used for computer simulations of classical systems. It acts on collisions with the walls of the container exclusively. It maps the incoming and outgoing…
It is an interesting open problem to achieve adaptive prescribed-time control for strict-feedback systems with unknown and fast or even abrupt time-varying parameters. In this paper we present a solution with the aid of several design and…
A general approach to modeling irreversibility starting from microscopic reversibility is presented. The time $t_s$ up to which relevant degrees of freedom of a system are tracked is extremely much shorter than the spectral resolution time…
Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…
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…
Recent investigations into the physical nature of information and fundamental limits to information transmission have revealed questions such as the possibility of superluminal data transfer or not; and whether reversible computation…
We study the time reversal of a general PDMP. The time reversed process is defined as $X_{(T-t)-}$, where $T$ is some given time and $X_t$ is a stationary PDMP. We obtain the parameters of the reversed process, like the jump intensity and…