Related papers: Nested sampling, statistical physics and the Potts…
We derive and validate a partition function for low-dimensional systems interacting with a heat bath, addressing the general issue of thermodynamic modeling of nanoscale systems. In contrast to bulk systems in the canonical (NVT) ensemble…
The fundamentals of Statistical Mechanics require a fresh definition in the context of the developments in Classical Mechanics of integrable and chaotic systems. This is done with the introduction of Micro Partitions ; a union of disjoint…
In the long-time pursuit of the solution to calculate the partition function (or free energy) of condensed matter, Monte-Carlo-based nested sampling should be the state-of-the-art method, and very recently, we established a direct integral…
The statistical mechanical interpretation of algorithmic information theory (AIT, for short) was introduced and developed in our former work [K. Tadaki, Local Proceedings of CiE 2008, pp.425-434, 2008], where we introduced the notion of…
Discrete random structures are important tools in Bayesian nonparametrics and the resulting models have proven effective in density estimation, clustering, topic modeling and prediction, among others. In this paper, we consider nested…
The aim of the present paper is to provide a preliminary investigation of the thermodynamics of particles obeying monotone statistics. To render the potential physical applications realistic, we propose a modified scheme called…
We introduce a new path integral Monte Carlo method for investigating nonadiabatic systems in thermal equilibrium and demonstrate an approach to reducing stochastic error. We derive a general path integral expression for the partition…
In performing a Bayesian analysis, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multi-modal or exhibit pronounced (curving) degeneracies.…
We formulate both Markov chain Monte Carlo (MCMC) sampling algorithms and basic statistical physics in terms of elementary symmetries. This perspective on sampling yields derivations of well-known MCMC algorithms and a new parallel…
A general method is presented for modeling high entropy alloys as ensembles of randomly sampled, ordered configurations on a given lattice. Statistical mechanics is applied post hoc to derive the ensemble properties as a function of…
The q-state Potts model is a fundamental framework in statistical physics and graph theory, with its partition function encoding rich information about spin configurations. The multivariate Tutte polynomial (known as the partition function…
We review and compare numerical methods that simultaneously control temperature while preserving the momentum, a family of particle simulation methods commonly used for the modelling of complex fluids and polymers. The class of methods…
The Potts model plays an essential role in classical statistical mechanics, illustrating many fundamental phenomena. One example is the existence of partially long-range-ordered states, in which some degrees of freedom remain disordered.…
Model comparison and calibrated uncertainty quantification often require integrating over parameters, but scalable inference can be challenging for complex, multimodal targets. Nested Sampling is a robust alternative to standard MCMC, yet…
One of the characteristic features of a stochastic process under resetting is that the probability density converges to a nonequilibrium stationary state (NESS). In addition, the approach to the stationary state exhibits a dynamical phase…
We present a novel statistical mechanics formalism for the theoretical description of the process of protein folding$\leftrightarrow$unfolding transition in water environment. The formalism is based on the construction of the partition…
The Potts model is a generalization of the Ising model with $Q>2$ components. In the fully connected ferromagnetic Potts model, a first-order phase transition is induced by varying thermal fluctuations. Therefore, the computational time…
Advances in techniques for thermal sampling in classical and quantum systems would deepen understanding of the underlying physics. Unfortunately, one often has to rely solely on inexact numerical simulation, due to the intractability of…
An exact analytical solution of generalized three-state double-chain Potts model with multi-spin interactions which are invariant under cyclic shift of all spin values is obtained. The partition function in a finite cyclically closed strip…
The nested distance builds on the Wasserstein distance to quantify the difference of stochastic processes, including also the information modelled by filtrations. The Sinkhorn divergence is a relaxation of the Wasserstein distance, which…