Related papers: Planck's Legacy to Statistical Mechanics
We begin our journey by recalling the fundamentals of Probability Theory that underlie one of its most significant applications to real-world problems: Parametric Estimation. Throughout the text, we systematically develop this theme by…
This is an overview of various aspects of the 6-vertex model in statistical mechanics and related models.
We review the connection between statistical mechanics and the analysis of random optimization problems, with particular emphasis on the random k-SAT problem. We discuss and characterize the different phase transitions that are met in these…
The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical…
Planck scale inspired theories which are also often accompanied with maximum energy and/or momentum scale predict deformed dispersion relations compared to ordinary special relativity and quantum mechanics. In this paper we resort to the…
In a recent letter, Christian Beck described a theoretical link between a family of stochastic differential equations and the probability density functions (PDF) derived from the formalism of nonextensive statistical mechanics. He applied…
An out of the box intellectual path exploring the foundations of quantum mechanics is discussed in some detail, in order to clarify why a possibly different way to look at the relevant fundamental questions can be identified and can support…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
Statistical physics is important in understanding the physics of interacting many bodies. This has been historically developed by attempts to understand colliding gases and quantifying quantities like entropy, free energy, and other…
Boltzmann's differential equation is replaced by the corresponding reciprocal symmetric finite difference equation. Finite difference translates discreteness of energy. Boltzmann's function, then, splits into two reciprocally related…
A brief review of the previous research on the Heisenberg uncertainty relations at the Planck scale is given. In this work, investigation of the uncertainty principle extends to p-adic and adelic quantum mechanics. In particular, p-adic…
Today it still remains a challenge whether quantum mechanics has an underlying statistical explanation or not. While there are and were a lot of models trying to explain quantum phenomena with statistical methods these all failed on certain…
We present a probabilistic extension of the description logic $\mathcal{ALC}$ for reasoning about statistical knowledge. We consider conditional statements over proportions of the domain and are interested in the probabilistic-logical…
Quantum mechanics appears to contain ghosts from both classical statistical mechanics and special relativity. On one hand, both the Dirac and Schr\"{o}dinger equations have classical analogs that emerge directly from classical statistical…
Hawking radiation is one of the cores in modern gratitational theory. Several articles have calculated the spectrum of Hawking radiation in Boltzmann-Gibbs statistical mechanics. However, based on recent researches, gravitational systems…
An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is…
The task of parametric model selection is cast in terms of a statistical mechanics on the space of probability distributions. Using the techniques of low-temperature expansions, we arrive at a systematic series for the Bayesian posterior…
In black hole physics, inflationary cosmology, and quantum field theories, it is conjectured that the physical laws are subject to radical changes below the Planck length. Such changes are due to effects of quantum gravity believed to…
In the background of a gravitational collapse, we compute the transition amplitudes for the creation of particles for distant observers due to higher-derivative interactions in addition to Hawking radiation. The amplitudes grow…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…