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We consider lattice-gas automata where the lack of semi-detailed balance results from node occupation redistribution ruled by distant configurations; such models with nonlocal interactions are interesting because they exhibit non-ideal gas properties and can undergo phase transitions. For this class of automata, mean-field theory provides a correct evaluation of properties such as compressibility and viscosity (away from the phase transition), despite the fact that no H-theorem strictly holds. We introduce the notion of locality — necessary to define quantities accessible to measurements — by treating the coupling between nonlocal bits as a perturbation. Then if we define operationally "local" states of the automaton — whether the system is in a homogeneous or in an inhomogeneous state — we can compute an estimator of the entropy and measure the local channel occupation correlations. These considerations are applied to a simple model with nonlocal interactions.

We present an outline description of some fundamental theoretical properties in the Digital Physics lattice-gas algorithm.

In [C. G. Weaver Found. Phys. 51, 1 (2021)], I showed that Boltzmann’s H-theorem does not face a significant threat from the reversibility paradox. I argue that my defense of the H-theorem against that paradox can be used yet again for the purposes of resolving the recurrence paradox without having to endorse heavy-duty statistical assumptions outside of the hypothesis of molecular chaos. As in [C. G. Weaver Found. Phys. 51, 1 (2021)], lessons from the history and foundations of physics reveal precisely how such resolution is achieved.

A new, wide class of relativistic stochastic processes is introduced. All relativistic processes considered so far in the literature (the Relativistic Ornstein–Uhlenbeck Process as well as the Franchi–Le Jan and the Dunkel–Hänggi processes) are members of this class. The stochastic equations of motion and the associated forward Kolmogorov equations are obtained for each process in the class. The corresponding manifestly covariant transport equation is also obtained. In particular, the manifestly covariant equations for the Franchi–Le Jan and the Dunkel–Hänggi processes are derived here for the first time. Finally, the manifestly covariant approach is used to prove a new H-theorem for all processes in the class.

The entropic lattice Boltzmann method (ELBM) is an excellent method of numerical stability among of different versions of the lattice Boltzmann method for the simulation of hydrodynamics, especially for wind field simulation application of power grid disaster conditions. In this paper, an efficient improved particle swarm optimization (PSO) algorithm is studied for optimizing calculation parameters to achieve load balancing of ELBM on nonuniform grids in a heterogeneous computing platform. We also introduce a new concept of multi-block ELBM on composite grids for realization of the ELBM simulations of incompressible driven cavity flow. These new approaches rely on a two-dimensional space-time interpolation and solving the relaxation time parameter by direct approximation optimization strategy to guarantee conservation. Our CPU–GPU implementation of multi-block ELBM based on the improved PSO algorithm not only exploits adequately multi-core CPU computing resources for load balancing, but also follows carefully optimized storage to increase coalesced access on a GPU platform. The three-dimensional-driven cavity flow simulations validate the proposed multi-block ELBM even with severely under-resolved grids. In addition, some performance metrics are investigated based on the implementations of different refined grids and threading blocks. These results exhibit the improved PSO algorithm of the ELBM method which can optimize computing resource parameters in heterogeneous platforms, and the present multi-block ELBM can substantially improve the accuracy and computational efficiency for viscous flow computations.

This paper deals with the presentation of a kinetic model for a suspension of identical hard spheres. Considering that the collisions between particles are instantaneous, binary, inelastic and taking the diameter of the spheres into account, a Boltzmann equation for the dispersed phase is proposed. It allows one to obtain the conservation of mass and momentum as well as, for slightly inelastic collisions, an H-theorem which conveys the irreversibility of the evolution. The problem of the boundary conditions for the Boltzmann equation is then introduced. From an anisotropic law of rebound characterizing the inelastic and non-punctual impact of a particle to the wall, a parietal behavior for the first moments of the kinetic equation is deduced.

For the Boltzmann equation with an external potential force depending only on the space variables, there is a family of stationary solutions, which are local Maxwellians with space dependent density, zero velocity and constant temperature. In this paper, we will study the nonlinear stability of these stationary solutions by using the energy method. The analysis combines the analytic techniques used for the conservation laws using the fluid-type system derived from the Boltzmann equation (cf. [14]) and the dissipative effects on the fluid and non-fluid components of the Boltzmann equation through the celebrated H-theorem. To our knowledge, this is the first result on the global classical solutions to the Boltzmann equation with external force and non-trivial large time behavior in the whole space.

It was first suggested by David Z. Albert that the existence of a real, physical non-unitary process (i.e., “collapse”) at the quantum level would yield a complete explanation for the Second Law of Thermodynamics (i.e., the increase in entropy over time). The contribution of such a process would be to provide a physical basis for the ontological indeterminacy needed to derive the irreversible Second Law against a backdrop of otherwise reversible, deterministic physical laws. An alternative understanding of the source of this possible quantum “collapse” or non-unitarity is presented herein, in terms of the Transactional Interpretation (TI). The present model provides a specific physical justification for Boltzmann’s often-criticized assumption of molecular randomness (Stosszahlansatz), thereby changing its status from an ad hoc postulate to a theoretically grounded result, without requiring any change to the basic quantum theory. In addition, it is argued that TI provides an elegant way of reconciling, via indeterministic collapse, the time-reversible Liouville evolution with the time-irreversible evolution inherent in so-called “master equations” that specify the changes in occupation of the various possible states in terms of the transition rates between them. The present model is contrasted with the Ghirardi–Rimini–Weber (GRW) “spontaneous collapse” theory previously suggested for this purpose by Albert.

In attempting to derive irreversible macroscopic thermodynamics from reversible microscopic dynamics, Boltzmann inadvertently smuggled in a premise that assumed the very irreversibility he was trying to prove: ‘molecular chaos’. The program of ‘einselection’ (environmentally induced superselection) within Everettian approaches faces a similar ‘Loschmidt’s Paradox’: the universe, according to the Everettian picture, is a closed system obeying only unitary dynamics, and it therefore contains no distinguishable environmental subsystems with the necessary ‘phase randomness’ to effect einselection of a pointer observable. The theoretically unjustified assumption of distinguishable environmental subsystems is the hidden premise that makes the derivation of einselection circular. In effect, it presupposes the ‘emergent’ structures from the beginning. Thus the problem of basis ambiguity remains unsolved in Everettian interpretations.

We develop quantitative measures of entropy evolution for particle systems undergoing collision process in relation with various instability properties.