What the Boltzmann money game teaches us about statistical mechanics (and maybe economics)

Dmitrii E. Makarov

Home/Archive/arXiv

arXiv · 2507.22180

What the Boltzmann money game teaches us about statistical mechanics (and maybe economics)

Dmitrii E. Makarov

View original source ↗Read source document ↗Export metadata ↓

Abstract

This note explains why a large class of fair, or reversible "money games", i.e., stochastic models of wealth redistribution among agents, lead to steady states described by canonical and microcanonical distributions. The games considered include, for example, ones where more than two agents can be simultaneously involved in money transfers (similarly to many-body collisions in chemical kinetics) and where amounts transferred between agents are random. At the same time, money games that break time reversal symmetry can also lead to the canonical/microcanonical distributions, as illustrated by an explicit example.

Explore related subjects

physics.chem-ph cond-mat.stat-mech

Keep this discovery

BibTeX RIS

Dmitrii E. Makarov. 2025-07-29. What the Boltzmann money game teaches us about statistical mechanics (and maybe economics). https://arxiv.org/abs/2507.22180

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Breaking Water at Graphene Defects

Water dissociation at solid surfaces underpins processes ranging from corrosion and catalysis to electrochemistry and photovoltaics. Defects often serve as reactive sites for dissociation, yet how solvation influences water dissociation at such sites remains poorly understood. Here, we use state-of-the-art machine-learned interatomic potentials to explore water dissociation at defective graphene-water interfaces. We show that solvation qualitatively changes the reaction mechanism at a graphene single vacancy (SV), opening pathways that are absent for an isolated water molecule. Whereas the gas-phase process proceeds via a single concerted channel, the solvated SV splits water through two competing pathways: a basic route forming SV-H and OH-(aq), and an acidic route forming SV-OH and H3O+(aq). These lower-barrier pathways produce distinct chemisorbed intermediates that enhance graphene-water adsorption. Accordingly, even a simple carbon vacancy gives rise to unexpectedly rich interfacial chemistry, coupling surface chemistry to interfacial charge and wettability, with implications for carbon functionalization and nanofluidic transport.

physics.chem-ph↗

arXiv2026

Comprehensive Study of L-Menthol and Octanoic Acid as a Hydrophobic Eutectic Solvent

Hydrophobic eutectic solvents (HES) based on natural compounds represent promising green alternatives to conventional solvents. In this work, we investigate the physicochemical, structural, and dynamical properties of an ES formed by L-menthol and octanoic acid using a combined experimental and molecular dynamics simulation approach. Five compositions with molar ratios from 1:3 to 3:1 were studied with molecular dynamics simulation in the temperature range 15 degrees C to 35 degrees C. Experimental measurements of density and viscosity in the temperature range from 5 degrees C to 35 degrees C were complemented with results obtained from MD simulations employing the OPLS force field. Structural analyses based on radial distribution functions and Kirkwood-Buff integrals reveal that the dominant interactions in the mixture are hydrogen bonds between L-menthol and octanoic acid molecules. Dynamic properties, including self-diffusion coefficients and hydrogen-bond lifetimes, indicate that intermolecular hydrogen bonds between the two components are stronger and longer-lived than bonds between identical species. These findings provide molecular-level insight into the structure and transport properties of menthol-based ESs relevant for green solvent applications.

physics.chem-ph↗

arXiv2026

More is not always better: Dissociative photoionization limits the EUV absorbing photacid generator pentafluorophenyl triflate in photolithography

Pentafluorophenyl triflate has been explored as a highly absorbing neutral photoacid generator (PAG) candidate for next generation chemically amplified resists used in extreme ultraviolet (EUV) lithography. Although increased fluorination enhances EUV absorption, this study demonstrates that such an approach does not necessarily improve photoacid generation efficiency. Using photoelectron-photoion coincidence (PEPICO) spectroscopy at the 92 eV photon energy of the EUV scanners in combination with quantum chemical calculations, the dissociative photoionization of pentafluorophenyl triflate was systematically investigated. The photoionization mass spectrum reveals extensive fragmentation, with the parent ion contributing only 3.1 % of the total signal and CF$_3^+$ representing the dominant product ion. Computed appearance energies align well with experimental trends and support a sequential fragmentation pathway involving loss of SO$_2$, CF$_3$, and CO. Crucially, none of the major dissociation channels yield precursors capable of forming triflic acid, the strong photoacid required for efficient deprotection reactions in chemically amplified resists. Combined with previous dissociative electron attachment studies indicating similarly unfavorable fragmentation, the results demonstrate that despite its high EUV absorption cross section, pentafluorophenyl triflate is unsuitable as a PAG for EUV lithography. The findings highlight the importance of understanding fundamental photoionization and electron interaction mechanisms to guide the rational design of next generation high performance EUV photoresists.

physics.chem-ph↗