Related Experiment Video
Updated: Aug 11, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Molecular dynamics ensemble, equation of state, and ergodicity
W W Wood1, J J Erpenbeck, G A Baker
1Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Summary
Researchers redefined the molecular dynamics ensemble to the NVEMR ensemble. This study tests the quasiergodic hypothesis for hard-sphere systems, finding it supported by the virial approach but only partially by the entropy approach.
Area of Science:
- Statistical Mechanics
- Computational Physics
- Thermodynamics
Background:
- The molecular dynamics ensemble, a variant of the NVE ensemble, was recently redefined to include a time-invariant function G and total linear momentum M.
- The NVEM ensemble has been used to study the equation of state for hard-sphere systems.
Purpose of the Study:
- To reformulate the molecular dynamics ensemble as the NVEMR ensemble, incorporating center-of-mass position.
- To investigate the equation of state for hard-sphere systems within this new ensemble.
- To test the quasiergodic hypothesis using both virial and entropy approaches.
Main Methods:
- Reformulation of the molecular dynamics ensemble to the NVEMR ensemble.
- Calculation of the equation of state using the virial function.
- Calculation of the equation of state using the Boltzmann entropy with two different definitions (theta=0 and theta=1).
- Comparison of results with existing molecular dynamics and Monte Carlo data for hard-disk systems.
Main Results:
- The virial approach in the NVEMR ensemble supports the quasiergodic hypothesis, consistent with previous findings in the NVEM ensemble.
- The entropy approach's support for the quasiergodic hypothesis depends on the definition of entropy used.
- The quasiergodic hypothesis is supported when entropy is defined via the phase integral over the energy sphere (theta=0).
- The quasiergodic hypothesis is not supported when entropy is defined via the phase integral over the energy shell (theta=1).
Conclusions:
- The NVEMR ensemble provides a framework for studying hard-sphere systems.
- The quasiergodic hypothesis is supported by the virial approach in the NVEMR ensemble.
- The validity of the quasiergodic hypothesis, when assessed through entropy, is sensitive to the specific definition of entropy employed.
Related Concept Videos
02:39Entropy
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
01:21Molecular Kinetic Energy
The word "gas" comes from the Flemish word meaning "chaos," first used to describe vapors by the chemist J. B. van Helmont. Consider a container filled with gas, with a continuous and random motion of molecules. During collisions, the velocity component parallel to the wall is unchanged, and the component perpendicular to the wall reverses direction but does not change in magnitude. If the molecule’s velocity changes in the x-direction, then its momentum is changed. During the short time of the...
01:18Entropy
The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
01:10Entropy Change in Reversible Processes
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
01:27Variables and Equations of State
The physical state of a pure substance can be defined by certain state variables such as volume (V), pressure (p), temperature (T), and amount of substance (n). When two gases are separated by a movable wall, the gas with the higher pressure naturally compresses the gas with the lower pressure. This causes the high-pressure gas to expand and the low-pressure gas to compress until both gases achieve mechanical equilibrium. At this point, their pressures equalize, and the movement of the wall...
01:14The Entropy as a State Function
Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...