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The critical point and the critical exponents for a phase transition can be determined using the Finite-Size Scaling (FSS) analysis. This method assumes that the phase transition occurs only in the infinite size limit. However, there has…
We define a class of stochastic processes based on evolutions and measurements of quantum systems, and consider the complexity of predicting their long-term behavior. It is shown that a very general class of decision problems regarding…
We study the extent to which \psi-epistemic models for quantum measurement statistics---models where the quantum state does not have a real, ontic status---can explain the indistinguishability of nonorthogonal quantum states. This is done…
We study a basic problem of approximating the size of an unknown set $S$ in a known universe $U$. We consider two versions of the problem. In both versions the algorithm can specify subsets $T\subseteq U$. In the first version, which we…
Starting from arbitrary sets of quantum states and measurements, referred to as the prepare-and-measure scenario, an operationally noncontextual ontological model of the quantum statistics associated with the prepare-and-measure scenario is…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
We study how the grand-canonical density matrix arises in macroscopic quantum systems. ``Canonical typicality'' is the known statement that for a typical wave function $\Psi$ from a micro-canonical energy shell of a quantum system $S$…
The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables,…
Physical systems are often neither completely closed nor completely open, but instead they are best described by dynamical systems with partial escape or absorption. In this paper we introduce classical measures that explain the main…
We study the process of observation (measurement), within the framework of a `perspectival' (`relational', `relative state') version of the modal interpretation of quantum mechanics. We show that if we assume certain features of…
This paper is devoted to the estimation of the minimal dimension P of the state-space realizations of a high-dimensional time series y, defined as a noisy version (the noise is white and Gaussian) of a useful signal with low rank rational…
Building upon a recent analysis of the measurement process in Hamiltonian mechanics, this article investigates the Bayesian epistemology of classical physics -- the landscape of accessible probability distributions over phase space. I prove…
We analyze a macroscopic model with a maximal density constraint which describes short range repulsion in biological systems. This system aims at modeling finite-size particles which cannot overlap and repel each other when they are too…
The letter submitted is an executive summary of our previous paper. To solve the Einstein Podolsky Rosen 'paradox' the two boundary quantum mechanics is taken as self consistent interpretation of quantum dynamics. The difficulty with this…
We present a classical algorithm that approximately samples from the output distribution of certain noisy Boson Sampling experiments. This algorithm is inspired by a recent result of Aharonov, Gao, Landau, Liu and Vazirani and makes use of…
Recent experimental advances have inspired the development of theoretical tools to describe the non-equilibrium dynamics of quantum systems. Among them an exact representation of quantum spin systems in terms of classical stochastic…
Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were…
In the framework of Gibbs statistical theory, the issue of the distribution of particle sizes forming the statistical system and the moments of this distribution are considered. This task is relevant for a wide variety of applications. The…
The onset of stochasticity is measured in $\Lambda$CDM cosmological simulations using a set of classical observables. It is quantified as the local derivative of the logarithm of the dispersion of a given observable (within a set of…
Decoherence is an essential mechanism that defines the boundary between classical and quantum behaviours, while imposing technological bounds for quantum devices. Little is known about quantum coherence of mechanical systems, as opposed to…