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Relevant and fundamental concepts of the statistical mechanical theory of classical liquids are ordinarily introduced in the context of the description of thermodynamic equilibrium states. This makes explicit reference to probability…
We describe a particular approach for the construction of a nonequilibrium statistical ensemble formalism for the treatment of dissipative many-body systems. This is the so-called Nonequilibrium Statistical Operator Method, based on the…
An equilibrium statistical system is known to be stable if the fluctuations of global observables are normal, when their dispersions are proportional to the number of particles, or to the system volume. A general theorem is rigorously…
This paper studies the stability of sampled and networked control systems with sampling and communication times governed by probabilistic clocks. The clock models have few restrictions, and can be used to model numerous phenomena such as…
Consistency and stability are two essential ingredients in the design of numerical algorithms for partial differential equations. Robust algorithms can be developed by incorporating nonlinear physical stability principles in their design,…
We study the classical non-equilibrium statistical mechanics of scalar field theory on the lattice. Steady states are analyzed near and far from equilibrium. The bulk thermal conductivity is computed, including its temperature dependence.…
In this work, we demonstrate how to reliably estimate epistemic uncertainty while maintaining the flexibility needed to capture complicated aleatoric distributions. To this end, we propose an ensemble of Normalizing Flows (NF), which are…
In this paper we present a self-contained macroscopic description of diffusive systems interacting with boundary reservoirs and under the action of external fields. The approach is based on simple postulates which are suggested by a wide…
We study a simple extension of the original Hartnoll, Herzog and Horowitz (HHH) holographic superfluid model with two nonlinear scalar self-interaction terms $\lambda |\psi|^4$ and $\tau |\psi|^6$ in the probe limit. Depending on the value…
The dynamics of a quantum system coupled to a classical environment and subject to constraints that drive it out of equilibrium is described. The evolution of the system is governed by the quantum-classical Liouville equation. Rather than…
Equilibrium canonical distribution in statistical mechanics assumes weak system-bath coupling (SBC). In real physical situations this assumption can be invalid and equilibrium quantum statistics of the system may be non-canonical. By…
The statistical properties of non-interacting bosons and fermions confined in trapping potentials are most easily obtained when the system may exchange energy and particles with a large reservoir (grand-canonical ensemble). There are…
An isolated quantum system is considered, prepared in a nonequilibrium initial state. In order to uniquely define the system dynamics, one has to construct a representative statistical ensemble. From the principle of least action it follows…
The critique against using Boltzmann's microcanonical entropy, an "ensemble measure", as foundation of statistics is rebuffed. The confusion of the microcanonical distribution with the exponential Boltzmann-Gibbs (``BG'') distribution is…
We present a predictive master spectrum describing turbulence-like flows in microfluidic systems. Extending Pao's viscous-range closure, the model introduces (i) an adaptive inertial-range slope dependent on measurable dimensionless numbers…
Boltzmann's principle S(E,N,V...)=ln W(E,N,V...) allows the interpretation of Statistical Mechanics of a closed system as Pseudo-Riemannian geometry in the space of the conserved parameters E,N,V... (the conserved mechanical parameters in…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and…
Depending on the exact experimental conditions, the thermodynamic properties of physical systems can be related to one or more thermostatistical ensembles. Here, we survey the notion of thermodynamic temperature in different statistical…
This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…