H-theorem at negative temperature: the random exchange model with bounds
arXiv:2312.12017 · doi:10.1088/1742-5468/ada49b
Abstract
Random exchange kinetic models are widely employed to describe the conservative dynamics of large interacting systems. Due to their simplicity and generality, they are quite popular in several fields, from statistical mechanics to biophysics and economics. Here we study a version where bounds on the individual shares of the globally conserved quantity are introduced. We analytically show that this dynamics allows stationary states with population inversion, described by Boltzmann statistics at negative absolute temperature if the conserved quantity has the physical meaning of an energy. The proposed model provides therefore a privileged system for the study of thermalization toward a negative temperature state. First, the genuine equilibrium nature of the stationary state is verified by checking the detailed balance condition. Then, an H-theorem is proven, ensuring that such equilibrium condition is reached by a monotonic increase of the Boltzmann entropy. We also provide analytical and numerical evidence that a large intruder in contact with the system thermalizes, suggesting a practical way to design a thermal bath at negative temperature.
15 pages, 2 figures
References in corpus (28)
- Scale-free correlations in bird flocks
- Stochastic thermodynamics under coarse-graining
- Negative Absolute Temperature for Motional Degrees of Freedom
- Giant Vortex Clusters in a Two-Dimensional Quantum Fluid
- Order from chaos: Observation of large-scale flow from turbulence in a two-dimensional superfluid
- Inconsistent thermostatistics and negative absolute temperatures
- The Nature of the Condensate in Mass Transport Models
- Money in Gas-Like Markets: Gibbs and Pareto Laws
- The Kinetics of Wealth and the Origin of the Pareto Law
- The nonequilibrium discrete nonlinear Schroedinger equation
- Statistical Mechanics of Systems with Negative Temperature
- Consistent description of fluctuations requires negative temperatures
- On the dispute between Boltzmann and Gibbs entropy
- Definition and relevance of nonequilibrium intensive thermodynamic parameters
- An theorem for Boltzmann's equation for the Yard-Sale Model of asset exchange
- Localization transition in the Discrete Non-Linear Schrödinger Equation: ensembles inequivalence and negative temperatures
- Marginal speed confinement resolves the conflict between correlation and control in natural flocks of birds
- Inexistence of equilibrium states at absolute negative temperatures
- A Chain, a Bath, a Sink and a Wall
- Construction of the factorized steady state distribution in models of mass transport
- Subdiffusion and dynamical heterogeneities in a lattice glass model
- About thermometers and temperature
- Langevin equation in systems with also negative temperatures
- Monotonic entropy growth for a nonlinear model of random exchanges
- Origin of Negative Temperatures in Systems Interacting with External Fields
- Derivation of a Langevin equation in a system with multiple scales: the case of negative temperatures
- A mass transport model with a simple non-factorized steady-state distribution
- Clausius inequality and H-theorems for some models of random wealth exchange