# The density of a fluid on a curved surface

@article{Fantoni2012TheDO, title={The density of a fluid on a curved surface}, author={Riccardo Fantoni}, journal={arXiv: Statistical Mechanics}, year={2012} }

We discuss the property of the number density of a fluid of particles living in a curved surface without boundaries to be constant in the thermodynamic limit. In particular we find a sufficient condition for the density to be constant along the Killing vector field generating a given isometry of the surface and the relevant necessary condition. We reinterpret the effect of a curvature on the fluid in a physical way as responsible of an external "force" acting on the particles.

## 4 Citations

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## References

SHOWING 1-10 OF 32 REFERENCES

Pressure and Maxwell Tensor in a Coulomb Fluid

- Physics
- 1999

The pressure in a classical Coulomb fluid at equilibrium is obtained from the Maxwell tensor at some point inside the fluid, by a suitable statistical average. For fluids in a Euclidean space, this…

Charge Fluctuations for a Coulomb Fluid in a Disk on a Pseudosphere

- Physics
- 2004

The classical (i.e., non-quantum) equilibrium statistical mechanics of a Coulomb fluid living on a pseudosphere (an infinite surface of constant negative curvature) is considered. The Coulomb fluid…

The two-dimensional Coulomb gas on a sphere: Exact results

- Physics
- 1992

At the special value of the reduced inverse temperatureΓ=2, the equilibrium statistical mechanics of a two-dimensional Coulomb gas confined to the surface of a sphere is an exactly solvable problem,…

Two-Dimensional Coulomb Systems on a Surface of Constant Negative Curvature

- Physics
- 1998

We study the equilibrium statistical mechanics of classical two-dimensional Coulomb systems living on a pseudosphere (an infinite surface of constant negative curvature). The Coulomb potential…

The two-dimensional two-component plasma plus background on a sphere: Exact results

- Physics
- 1996

An exact solution is given for a two-dimensional model of a Coulomb gas, more general than the previously solved ones. The system is made up of a uniformly charged background, positive particles, and…

Statistical Mechanics of Liquids and Fluids in Curved Space

- Physics, Mathematics
- 2011

In this article, we review the progress made on the statistical mechanics of liquids and fluids embedded in curved space. Our main focus will be on two-dimensional manifolds of constant nonzero…

Two-Dimensional One-Component Plasma on Flamm’s Paraboloid

- Physics
- 2008

We study the classical non-relativistic two-dimensional one-component plasma at Coulomb coupling Γ=2 on the Riemannian surface known as Flamm’s paraboloid which is obtained from the spatial part of…

Pressures for a One-Component Plasma on a Pseudosphere

- Physics
- 2002

The classical (i.e., non-quantum) equilibrium statistical mechanics of a two-dimensional one-component plasma (a system of charged point-particles embedded in a neutralizing background) living on a…

A Monte Carlo study of the classical two-dimensional one-component plasma

- Physics
- 1982

We present results from extensive Monte Carlo simulations of the fluid phase of the two-dimensional classical one-component plasma (OCP). The difficulties associated with the infinite range of the…

Exact Statistical Mechanics of a One‐Dimensional System with Coulomb Forces. II. The Method of Functional Integration

- Mathematics
- 1962

The statistical mechanics of a one‐dimensional system of charged sheets is studied in the formalism of the grand canonical ensemble. It is shown that the grand partition function may be expressed as…