Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0503251

Self-gravitating Brownian systems and bacterial populations with two or more types of particles

Julien Sopik·Clement Sire·Pierre-Henri Chavanis
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the thermodynamical properties of a self-gravitating gas with two or more types of particles. Using the method of linear series of equilibria, we determine the structure and stability of statistical equilibrium states in both microcanonical and canonical ensembles. We show how the critical temperature (Jeans instability) and the critical energy (Antonov instability) depend on the relative mass of the particles and on the dimension of space. We then study the dynamical evolution of a multi-components gas of self-gravitating Brownian particles in the canonical ensemble. Self-similar solutions describing the collapse below the critical temperature are obtained analytically. We find particle segregation, with the scaling profile of the slowest collapsing particles decaying with a non universal exponent that we compute perturbatively in different limits. These results are compared with numerical simulations of the two-species Smoluchowski-Poisson system. Our model of self-attracting Brownian particles also describes the chemotactic aggregation of a multi-species system of bacteria in biology.

Explore related subjects

cond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Julien Sopik, Clement Sire, Pierre-Henri Chavanis. 2005-03-10. Self-gravitating Brownian systems and bacterial populations with two or more types of particles. https://doi.org/10.1103/physreve.72.026105

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

KEEP EXPLORING

Related papers

arXiv2026

Competition for Survival and the Law of Maximum Entropy Production

The law of maximum entropy production (LMEP) is a selection principle stating that a non-equilibrium system will select the path or assembly of paths out of available paths that minimizes the potential or maximizes the entropy at the fastest rate given the constraints. Precise quantitative experimental tests are desirable for LMEP verification. Here we report electrical-circuit experiments on suspensions of silver particles which self-organize under electric field, form conducting paths and thus generate entropy by Joule heating. Our experiments on parallel-connected pairs of samples demonstrate a competitive relationship, thereby supporting the selection of the most efficient path. We find: (1) With sufficient voltage, a conducting bundle of silver particles forms, which acts as a self-organized dissipative structure (SODS). (2) With two samples in parallel, usually only one can develop SODS, due to the competition effect. As one sample approaches the maximum EPR, the others EPR is near zero. This confirms the path selection principle: only the highest EPR path survives. (3) At the end of the evolution, the sum of the sample EPR and the power supply circuit EPR approaches the calculated maximum. The deviation from the maximum is slightly lower when there are two competing samples. We identify the selection mechanism enabling natural selection and LMEP: A SODS gains a form of physical "fitness" when it establishes a pathway that efficiently suppresses the driving thermodynamic potential. As it develops and approaches the maximum EPR, the SODS modifies its nonequilibrium environment by consuming available free energy and eliminating the gradients that could support alternative pathways. We also examine the global implications of LMEP and propose that it serves as a driving mechanism propelling the hypothetical ascent of civilizations along the Kardashev scale.

cond-mat.stat-mech↗
arXiv2026

Measurement-induced spatially nonuniform fluctuations of the local particle number and their crossover in a quasiperiodic free-fermion chain

We study continuously monitored dynamics of a quasiperiodic free-fermion chain defined on a Fibonacci lattice. We focus on fluctuations of the local particle number, which do not exhibit quasiperiodic spatial modulation in the unitary limit. Remarkably, we demonstrate that they exhibit a nonuniform spatial pattern originating from the quasiperiodic long-range order under continuous measurement. Furthermore, employing both physicaland perpendicular-space analyses, we elucidate that a measurement-induced crossover emerges in fluctuations due to the interplay between the incommensurate modulation and the continuous measurement. While weak measurement yields a distribution reflecting the long-range spatial structure of the quasiperiodic system, an increase in measurement strength alters the distribution into one dominated by the local environment of each site. A structure-factor analysis further reveals that the weak-measurement regime is characterized by two dominant Bragg peaks corresponding to the golden-mean modulation, whereas the strong-measurement regime exhibits the characteristic Bragg-peak hierarchy of the Fibonacci pattern. We also elucidate that the measurement-induced crossover emerges in other physical quantities such as connected correlation functions. These findings offer insights into nonequilibrium quasiperiodic phenomena emerging in continuously monitored dynamics.

cond-mat.stat-mech↗
arXiv2026

Entanglement Asymmetry in Random Quantum Automata

We investigate the subsystem entanglement asymmetry in random quantum automaton ensembles, which are generated by permuting the basis states in the Hilbert space and applying global phase shifts. We compute the ensemble average of the $U(1)$ subsystem asymmetry in different connectivity geometries, showing that the late-time limit of the ensemble associated to a 2-local circuit geometry coincides with the all-to-all ensemble average. By focusing on different subsystem sizes, we demonstrate that, similarly to Haar-random circuits, the system locally symmetrizes. However, in sharp contrast to the Haar-random setting, the scale at which symmetrization happens depends on the initial state, a phenomenon we associate with the interplay of conservation of the participation entropy and the uniform exploration of charge sectors. Additionally, we connect the growth of the subsystem asymmetry to the subsystem coherence and show that their growth is characterized by the same symmetrization scale.

cond-mat.stat-mech↗