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There are three levels of description in classical statistical mechanics, the microscopic/dynamic, the macroscopic/statistical and the thermodynamic. At one end there is a well-used concept of equilibrium in thermodynamics and at the other…
We study the equilibration properties of classical integrable field theories at a finite energy density, with a time evolution that starts from initial conditions far from equilibrium. These classical field theories may be regarded as…
This paper presents a universal representation of symmetric (permutation-invariant) functions with multidimensional variable-size variables. These representations help justify approximation methods that aggregate information from each…
We identify a recently proposed shifting operation on classical phase space as a gauge transformation for statistical mechanical microstates. The infinitesimal generators of the continuous gauge group form a non-commutative Lie algebra,…
In order to better understand a complex theory like quantum mechanics, it is sometimes useful to take a step back and create alternative theories, with more intuitive foundations, and examine which features of quantum mechanics can be…
We analyze a simple classical Hamiltonian system within the hypothesis of renormalizability and isotropy that essentially led Maxwell to his ubiquitous Gaussian distribution of velocities. We show that the equilibrium-like power-law energy…
To develop a systematic treatment of the self-interaction problem in classical gauge theories and general relativity, we study tenable manifestations of self-interaction: topological phases, and rearrangements of degrees of freedom…
Any metric theory of gravity whose interaction with quantum particles is described by a covariant wave equation is equivalent to a vector theory that satisfies Maxwell-type equations identically. This result does not depend on any…
The explicit incorporation of task-specific inductive biases through symmetry has emerged as a general design precept in the development of high-performance machine learning models. For example, group equivariant neural networks have…
The Boltzmann and Gibbs approaches to statistical mechanics have very different definitions of equilibrium and entropy. The problems associated with this are discussed and it is suggested that they can be resolved, to produce a version of…
An extension of the Lorentz group that includes generators $\Gamma^\mu$ carrying a space-time index has been previously demonstrated to \emph{explicitly} construct the Minkowski metric \emph{within} the internal group space as a consequence…
We describe in detail a mathematical framework in which statistical ensembles of hybrid classical-quantum systems can be properly described. We show how a maximum entropy principle can be applied to derive the microcanonical ensemble of…
Equilibrium statistical mechanics provides powerful tools to understand physics at the macroscale. Yet, the question remains how this can be justified based on a microscopic quantum description. Here, we extend the ideas of pure state…
We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For…
Predicting the stationary behavior of observables in isolated many-body quantum systems is a central challenge in quantum statistical mechanics. While one can often use the Gibbs ensemble, which is simple to compute, there are many…
The question of how irreversibility can emerge as a generic phenomena when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the…
A central task of artificial intelligence is the design of artificial agents that act towards specified goals in partially observed environments. Since such environments frequently include interaction over time with other agents with their…
A problem of the equivalence of statistical ensembles is critically analyzed. It is shown, that although different probability distributions of statistical physics have the same behavior in the thermodynamic limit, there are physical…
A simple minimalist argument is given for why some correlations between quantum systems boggle our classical intuition. The argument relies on two elementary physical assumptions, and recovers the standard experimentally-testable Bell…
A macroscopic quantum model of a two-level system (the analogue of a half-spin particle) is described. The model is employed for simulating not only the system under study, but the measurement process as well. Single- and two-particle state…