Related papers: Statistical Mechanics of Unconfined Systems: Chall…
The paper moves a step towards the full integration of statistical mechanics and information theory. Starting from the assumption that the thermodynamical system is composed by particles whose quantized energies can be modelled as…
We consider dynamical systems evolving near an equilibrium statistical state where the interest is in modelling long term behavior that is consistent with thermodynamic constraints. We adjust the distribution using an entropy-optimizing…
The existence of the {\em typical set} is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of…
A simplified thermodynamic approach of the incompressible 2D Euler equation is considered based on the conservation of energy, circulation and microscopic enstrophy. Statistical equilibrium states are obtained by maximizing the…
There are two main approaches to non-equlibrium statistical mechanics: one using stochastic processes and the other using dynamical systems. To model the dynamics during inflation one usually adopts a stochastic description, which is known…
Confined active particles constitute simple, yet realistic, examples of systems that converge into a non-equilibrium steady state. We investigate a run-and-tumble particle in one spatial dimension, trapped by an external potential, with a…
In the works on Statistical Mechanics and Statistical Physics, when deriving the distribution of particles of ideal gases, one uses the method of Lagrange multipliers in a formal way. In this paper we treat rigorously this problem for…
We consider a Statistical Mechanics approach to granular systems by following the original ideas developed by Edwards. We use the concept of ``inherent states'', defined as the stable configurations in the potential energy landscape,…
In this paper, a simple case of Bayesian mechanics under the free energy principle is formulated in axiomatic terms. We argue that any dynamical system with constraints on its dynamics necessarily looks as though it is performing inference…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
In urban environments, parking has proven to be a significant source of congestion and inefficiency. In this study, we propose a methodology that offers a systematic solution to minimize the time spent by drivers in finding parking spaces.…
In this work, we show a connection between superstatistics and position-dependent mass (PDM) systems in the context of the canonical ensemble. The key point is to set the fluctuation distribution of the inverse temperature in terms od the…
We study the statistical properties of the entropic optimal (self) transport problem for smooth probability measures. We provide an accurate description of the limit distribution for entropic (self-)potentials and plans as the…
We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concentration inequalities for dynamical systems using an entirely…
We study one-dimensional spinless fermions with random interactions, but without any on-site disorder. We find that random interactions generically stabilize a many-body localized phase, in spite of the completely extended single-particle…
By using dissipativity approach, we establish the stability condition for the feedback connection of a deterministic dynamical system $\Sigma$ and a stochastic memoryless map $\Psi$. After that, we extend the result to the class of large…
We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…
This paper considers a distributed stochastic optimization problem where the goal is to minimize the time average of a cost function subject to a set of constraints on the time averages of a related stochastic processes called penalties. We…
We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the…
We consider a stochastic process which is (a) described by a continuous-time Markov chain on only short time-scales and (b) constrained to conserve a number of hidden quantities on long time-scales. We assume that the transition matrix of…