Related papers: Probabilities and Path-Integral Realization of Exc…
In low-dimensional systems, indistinguishable particles can display statistics that interpolate between bosons and fermions. Signatures of these "anyons" have been detected in two-dimensional quasiparticle excitations of the fractional…
In causal inference, and specifically in the \textit{Causes of Effects} problem, one is interested in how to use statistical evidence to understand causation in an individual case, and so how to assess the so-called {\em probability of…
A generalization of the Van der Waals excluded volume procedure for the multicomponent hadron gas is proposed. The derivation is based on the grand canonical partition function for the system of particles of several species interacting by…
This paper calculates probability distributions modeling the Luria-Delbr\"uck experiment. We show that by thinking purely in terms of generating functions, and using a 'backwards in time' paradigm, that formulas describing various…
Microcanonical thermodynamics allows the application of statistical mechanics both to finite and even small systems and also to the largest, self-gravitating ones. However, one must reconsider the fundamental principles of statistical…
A discrete formulation of the real-time path integral as the expectation value of a functional of paths with respect to a complex probability on a sample space of discrete valued paths is explored. The formulation in terms of complex…
We consider the generalized exclusion statistics in the Kondo problem. The thermodynamic Bethe ansatz equations have been used for a multicomponent system of particles obeying the generalized exclusion principle. We have found a relation…
In this paper we show that the existence of a primarily discrete space-time may be a fruitful assumption from which we may develop a new approach of statistical thermodynamics in pre-relativistic conditions. The discreetness of space-time…
An analytical method to compute thermodynamic properties of a given Hamiltonian system is proposed. This method combines ideas of both dynamical systems and ensemble approaches to thermodynamics, providing de facto a possible alternative to…
Equilibrium statistical physics is considered from the point of view of statistical estimation theory. This involves the notions of statistical model, of estimators, and of exponential family. A useful property of the latter is the…
The low temperature physics of disordered systems is governed by the statistics of extremely low energy states. It is thus rather important to discuss the possible universality classes for extreme value statistics. We compare the usual…
Conventional thermo-statistics address infinite homogeneous systems within the canonical ensemble. However, some 170 years ago the original motivation of thermodynamics was the description of steam engines, i.e. boiling water. Its essential…
This is mainly a survey, explaining how the probabilistic (statistical mechanical) construction of Kahler-Einstein metrics on compact complex manifolds, introduced in a series of works by the author, naturally arises from classical…
We present a study of both the ``Iterative Procedure'' and the ``$\beta \to \beta'$ transformation'', proposed by Tsallis et al (Physica A261, 534) to find the probabilities $p_i$ of a system to be in a state with energy $\epsilon_i$,…
Real world scenarios can be captured with lifted probability distributions. However, distributions are usually encoded in a table or list, requiring an exponential number of values. Hence, we propose a method for extracting first-order…
Among the statistical mechanical frameworks able to describe systems in non-equilibrium steady states such as collisionless plasmas, self-gravitating systems and other complex systems, superstatistics have gained recent attention.…
Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation.…
Many AI researchers argue that probability theory is only capable of dealing with uncertainty in situations where a full specification of a joint probability distribution is available, and conclude that it is not suitable for application in…
For nearly any challenging scientific problem evaluation of the likelihood is problematic if not impossible. Approximate Bayesian computation (ABC) allows us to employ the whole Bayesian formalism to problems where we can use simulations…
We derive universal bounds for the finite-time survival probability of the stochastic work extracted in steady-state heat engines and the stochastic heat dissipated to the environment. We also find estimates for the time-dependent…