Related papers: Statistical mechanics guides the motions of cm sca…
Boltzmann's Principle S = k ln W was repeatedly criticized by Einstein since it lacked a proper dynamical foundation in view of the thermal motion of the particles, out of which a physical system consists. This suggests, in particular, that…
Boltzmann machine is a powerful tool for modeling probability distributions that govern the training data. A thermal equilibrium state is typically used for Boltzmann machine learning to obtain a suitable probability distribution. The…
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…
The Boltzmann equation is a nonlinear partial differential equation that plays a central role in statistical mechanics. From the mathematical point of view, the existence of global smooth solutions for arbitrary initial data is an…
Motion under stochastic resetting serves to model a myriad of processes in physics and beyond, but in most cases studied to date resetting to the origin was assumed to take zero time or a time decoupled from the spatial position at the…
In this paper physical multi-scale processes governed by their own principles for evolution or equilibrium on each scale are coupled by matching the stored and dissipated energy, in line with the Hill-Mandel principle. In our view the…
There exists a wide variety of works on the dynamics of large populations ranging from simple heuristic modeling to those based on advanced computer supported methods. Their interconnections, however, remain mostly vague, which…
The concentration of measure phenomena were discovered as the mathematical background of statistical mechanics at the end of the XIX - beginning of the XX century and were then explored in mathematics of the XX-XXI centuries. At the…
A critical step in data analysis for many different types of experiments is the identification of features with theoretically defined shapes in N-dimensional datasets; examples of this process include finding peaks in multi-dimensional…
We define a message-passing algorithm for computing magnetizations in Restricted Boltzmann machines, which are Ising models on bipartite graphs introduced as neural network models for probability distributions over spin configurations. To…
By detailed Molecular Dynamics and Monte Carlo simulations %of a realistic model we show that granular materials at rest can be described as thermodynamics systems. First we show that granular packs can be characterized by few parameters,…
We discuss several ways of illustrating fundamental concepts in statistical and thermal physics by considering various models and algorithms. We emphasize the importance of replacing students' incomplete mental images by models that are…
Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer…
Random packings of objects of a particular shape are ubiquitous in science and engineering. However, such jammed matter states have eluded any systematic theoretical treatment due to the strong positional and orientational correlations…
Coupled length and time scales determine the dynamic behavior of polymers and underlie their unique viscoelastic properties. To resolve the long-time dynamics it is imperative to determine which time and length scales must be correctly…
This study shows that the generalized Boltzmann distribution is the only distribution mathematically consistent with thermodynamics when the system is described by an ensemble of a certain mathematical form. This mathematical form is very…
We compare numerical and experimental results exploring the behaviour of liquid drops moving across a surface patterned with hydrophobic and hydrophilic stripes. A lattice Boltzmann algorithm is used to solve the hydrodynamic equations of…
We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at…
Many stochastic physical systems evolve smoothly over time in the sense that the distribution of states changes regularly across time steps. The transition from current state to the next state can often be modeled as the combination of a…
We consider stochastic thermodynamics as a theory of statistical inference for experimentally observed fluctuating time-series. To that end, we introduce a general framework for quantifying the knowledge about the dynamical state of the…