# Entropy growth during free expansion of an ideal gas

@inproceedings{Chakraborti2021EntropyGD, title={Entropy growth during free expansion of an ideal gas}, author={Subhadip Chakraborti and Abhishek Dhar and Sheldon Goldstein and Anupam Kundu and Joel L Lebowitz}, year={2021} }

To illustrate Boltzmann’s construction of an entropy function that is defined for a single microstate of a system, we present here the simple example of the free expansion of a one dimensional gas of hard point particles. The construction requires one to define macrostates, corresponding to macroscopic observables. We discuss two different choices, both of which yield the thermodynamic entropy when the gas is in equilibrium. We show that during the free expansion process, both the entropies…

## Figures from this paper

## 2 Citations

Fluctuation theorem for irreversible entropy production in electrical conduction.

- PhysicsPhysical review. E
- 2022

Linear irreversible thermodynamics predicts that the entropy production rate can become negative. We demonstrate this prediction for metals under AC driving whose conductivity is well described by…

Fluctuation theorem for irreversible entropy production in electrical conduction

- Economics
- 2021

M. V. S. Bonan¸ca acknowledges financial support from
FAPESP (Funda¸c˜ao de Amparo `a Pesquisa do Estado de
S˜ao Paulo) (Brazil) (Grant No. 2020/02170-4).

## References

SHOWING 1-10 OF 61 REFERENCES

Initial growth of Boltzmann entropy and chaos in a large assembly of weakly interacting systems

- Physics, Computer Science
- 2007

On the Nonequilibrium Entropy of Large and Small Systems

- PhysicsStochastic Dynamics Out of Equilibrium
- 2019

Thermodynamics makes definite predictions about the thermal behavior of macroscopic systems in and out of equilibrium. Statistical mechanics aims to derive this behavior from the dynamics and…

Gibbs and Boltzmann Entropy in Classical and Quantum Mechanics

- Physics
- 2019

The Gibbs entropy of a macroscopic classical system is a function of a probability distribution over phase space, i.e., of an ensemble. In contrast, the Boltzmann entropy is a function on phase…

Boltzmann entropy for dense fluids not in local equilibrium.

- PhysicsPhysical review letters
- 2004

It is argued that for isolated Hamiltonian systems monotonicity of S(M(t))=S (M(X(t))) should hold generally for "typical" (the overwhelming majority of) initial microstates (phase points) X0 belonging to the initial macrostate M0, satisfying M(X0)=M(0).

Heat conduction and entropy production in a one-dimensional hard-particle gas.

- PhysicsPhysical review letters
- 2002

Large scale simulations for a one-dimensional chain of hard-point particles with alternating masses are presented and why the system leads nevertheless to energy dissipation and entropy production, in spite of not being chaotic in the usual sense is discussed.

From Time-symmetric Microscopic Dynamics to Time-asymmetric Macroscopic Behavior: An Overview

- Physics
- 2007

Time-asymmetric behavior as embodied in the second law of thermodynamics is observed in {\it individual macroscopic} systems. It can be understood as arising naturally from time-symmetric microscopic…

Incomplete Thermalization from Trap-Induced Integrability Breaking: Lessons from Classical Hard Rods.

- PhysicsPhysical review letters
- 2018

A one-dimensional gas of hard rods trapped in a harmonic potential, which breaks integrability of the hard-rod interaction in a nonuniform way, is studied and three distinct regimes are found: initial, chaotic, and stationary.

From anomalous energy diffusion to levy walks and heat conductivity in one-dimensional systems

- Physics
- 2005

The evolution of infinitesimal, localized perturbations is investigated in a one-dimensional diatomic gas of hard-point particles (HPG) and thereby connected to energy diffusion. As a result, a Levy…

Hydrodynamic Limit for a Disordered Harmonic Chain

- PhysicsCommunications in Mathematical Physics
- 2018

We consider a one-dimensional unpinned chain of harmonic oscillators with random masses. We prove that after hyperbolic scaling of space and time the distributions of the elongation, momentum, and…