Related papers: The Ergodic Hypothesis: A Typicality Statement
The aim of this work is to put forward a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. After showing the formal equivalence linking econometric multinomial logit models to equilibrium…
Assuming that a threshold Ornstein-Uhlenbeck process is observed at discrete time instants, we propose generalized moment estimators to estimate the parameters. Our theoretical basis is the celebrated ergodic theorem. To use this theorem we…
For a quantum-mechanical counting process we show ergodicity, under the condition that the underlying open quantum system approaches equilibrium in the time mean. This implies equality of time average and ensemble average for correlation…
We propose a theory that describes quantitatively the (in)stability of fully MBL systems due to ergodic, i.e. delocalized, grains, that can be for example due to disorder fluctuations. The theory is based on the ETH hypothesis and…
The vast majority of the literature on learning dynamical systems or stochastic processes from time series has focused on stable or ergodic systems, for both Bayesian and frequentist inference procedures. However, most real-world systems…
Recently, T. Tao gave a finitary proof a convergence theorem for multiple averages with several commuting transformations and soon later, T. Austin gave an ergodic proof of the same result. Although we give here one more proof of the same…
In order to describe the properties of the observed distribution of wealth in a population, most economic models rely on the existence of an asymptotic equilibrium state. In addition, the process generating the equilibrium distribution is…
The Boltzmann equation is an integro-differential equation which describes the density function of the distribution of the velocities of the molecules of dilute monoatomic gases under the assumption that the energy is only transferred via…
This paper proposes a theory that bridges classical analytical mechanics and nonequilibrium thermodynamics. Its intent is to derive the evolution equations of a system from a stationarity principle for a suitably augmented Lagrangian…
The domain of validity of standard thermodynamics and Boltzmann-Gibbs statistical mechanics is discussed and then formally enlarged in order to hopefully cover a variety of anomalous systems. The generalization concerns {\it nonextensive}…
In the course of computer modeling of the most probable stationary macrostates of non-ergodic closed systems, a forecast was obtained about the existence of limits of applicability of the basic axiomatic postulate of statistical physics,…
We study an intermittent quasistatic dynamical system composed of nonuniformly hyperbolic Pomeau--Manneville maps with time-dependent parameters. We prove an ergodic theorem which shows almost sure convergence of time averages in a certain…
The study considers advantages of the introduced measure of time based on the entropy change under irreversible processes (entropy production). Using the example of non-equilibrium expansion of an ideal gas in vacuum, such a measure is…
Several results of black holes thermodynamics can be considered as firmly founded and formulated in a very general manner. From this starting point we analyse in which way these results may give us the opportunity to gain a better…
We study the possibility of applying statistical mechanics to generally covariant quantum theories with a vanishing Hamiltonian. We show that (under certain appropiate conditions) this makes sense, in spite of the absence of a notion of…
The dissertation describes ergodic properties of some stochastic dynamical systems generated by Markov chains with values in the state space which is a Polish space. The mathematical model describing the process of cell division is…
We have presented first an axiomatic derivation of Boltzmann entropy on the basis of two axioms consistent with two basic properties of thermodynamic entropy. We have then studied the relationship between Boltzmann entropy and information…
This paper is concerned with the ergodic subspaces of the state spaces of isolated quantum systems. We prove a new ergodic theorem for closed quantum systems which shows that the equilibrium state of the system takes the form of a grand…
We suggest employing log-ergodic processes to simulate the velocity of money in an ergodic manner. Our approach sheds light on economic behavior, policy implications, and financial dynamics by maintaining long-term stability. By bridging…
Many physicists think that the maximum entropy formalism is a straightforward application of Bayesian statistical ideas to statistical mechanics. Some even say that statistical mechanics is just the general Bayesian logic of inductive…