Related Experiment Video
Updated: May 10, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Sigma method for the microcanonical entropy or density of states
1Department of Chemistry and Molecular Biology, University of Gothenburg, SE-412 96 Gothenburg, Sweden. rasmusp@chem.gu.se
Summary
This study presents an improved method for calculating equilibrium entropy differences, offering superior accuracy for closely spaced energy levels and importance sampling Monte Carlo. Adjustments for molecular dynamics simulations are also discussed.
Area of Science:
- Statistical Mechanics
- Computational Chemistry
Background:
- Calculating equilibrium entropy differences is crucial for understanding molecular systems.
- Davis's method provides a framework for these calculations but has limitations.
Purpose of the Study:
- To introduce a simple yet effective improvement to Davis's method for calculating equilibrium entropy differences.
- To demonstrate the enhanced performance of the modified method under specific conditions.
Main Methods:
- The study refines the microcanonical averaging step within Davis's original method.
- Importance sampling Monte Carlo techniques are employed for averaging.
- The improved method's applicability to molecular dynamics simulations is investigated.
Main Results:
- The modified method shows superior performance compared to the original, particularly for closely spaced energy levels.
- Enhanced accuracy is achieved when using importance sampling Monte Carlo for microcanonical averaging.
- Guidelines for adapting the method for molecular dynamics simulations are provided.
Conclusions:
- The proposed modification offers a more robust and accurate approach to calculating equilibrium entropy differences.
- The findings are relevant for computational studies involving systems with closely spaced energy levels.
- The work facilitates the application of entropy difference calculations in molecular dynamics simulations.
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...
01:18Entropy
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...
02:38Third Law of Thermodynamics
A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
01:20Entropy and the Second Law of Thermodynamics
The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
01:26Entropy and the Second Law of Thermodynamics
Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...
01:23Absolute Entropies and the Third Law of Thermodynamics
Ludwig Edward Boltzmann developed a definition for entropy, which stated that absolute entropy is proportional to the natural logarithm of the number of possible combinations of particles. Entropy stands alone among state functions as the only one whose absolute values can be determined.Consider a gas sample confined to a container. As the container expands, the energy levels of gas molecules become more closely spaced. This increases the number of available energy states, thereby increasing...