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Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
For any dynamical system $T:X\rightarrow X$ of a compact metric space $X$ with $g-$almost product property and uniform separation property, under the assumptions that the periodic points are dense in $X$ and the periodic measures are dense…
Bilinear dynamical systems are ubiquitous in many different domains and they can also be used to approximate more general control-affine systems. This motivates the problem of learning bilinear systems from a single trajectory of the…
We study the properties of the random quantum states induced from the uniformly random pure states on a bipartite quantum system by taking the partial trace over the larger subsystem. Most of the previous studies have adopted a viewpoint of…
We study a system of two-mode stochastic oscillators coupled through their collective output. As a function of a relevant parameter four qualitatively distinct regimes of collective behavior are observed. In an extended region of the…
We present a theory for the steady-state dynamics of a two-dimensional system of spherically symmetric active Brownian particles. The derivation of the theory consists of two steps. First, we integrate out the self-propulsions and obtain a…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
A causal input-output system may be described by a function space for inputs, a function space for outputs, and a causal operator mapping the input space into the output space. A particular representation of the state of such a system at…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…
We establish that the nonequilibrium dynamics of most pure states gives rise to the same entropy production as that of the corresponding ensemble, provided the effective dimension of the ensemble is large enough. This establishes the…
It is shown how classical states, meant as states representing a classical object, can be produced in the thermodynamic limit, retaining the unitary evolution of quantum mechanics. Besides, using a simple model of a single spin interacting…
We provide a numerical study of the macroscopic model of [3] derived from an agent-based model for a system of particles interacting through a dynamical network of links. Assuming that the network remodelling process is very fast, the…
One way to look for complex behaviours in many-body quantum systems is to let the number $N$ of degrees of freedom become large and focus upon collective observables. Mean-field quantities scaling as $1/N$ tend to commute, whence complexity…
In a first part the scope of classical thermodynamics and statistical mechanics is discussed in the broader context of formal dynamical systems, including computer programmes. In this context classical thermodynamics appears as a particular…
The non-extensive statistical mechanics has been applied to describe a variety of complex systems with inherent correlations and feedback loops. Here we present a dynamical model based on previously proposed static model exhibiting in the…
A growing number of dynamical situations involve the coupling of particles or singularities with physical waves. In principle these situations are very far from the wave-particle duality at quantum scale where the wave is probabilistic by…
Consider a mixed quantum mechanical state, describing a statistical ensemble in terms of an arbitrary density operator $\rho$ of low purity, $\tr\rho^2\ll 1$, and yielding the ensemble averaged expectation value $\tr(\rho A)$ for any…