Related Experiment Video
Updated: Aug 5, 2026
09:23
Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
Quantum Microcanonical Entropy, Boltzmann's Equation, and the Second Law
Phillip C Lotshaw1, Michael E Kellman1
1Department of Chemistry and Biochemistry and Institute of Theoretical Science , University of Oregon Eugene , Oregon 97403 , United States.
The Journal of Physical Chemistry. A
|December 15, 2018
Summary
Researchers developed a quantum entropy concept for realistic temperature baths, finding "excess entropy production" due to quantum effects. This excess diminishes with weaker system-environment coupling, validating the quantum microcanonical ensemble.
Area of Science:
- Quantum thermodynamics
- Statistical mechanics
- Physical chemistry
Background:
- Classical microcanonical ensemble relies on the relation TΔS = ΔF.
- Quantum systems require a generalized entropy formulation for realistic environments.
- Previous models lacked applicability to temperature baths.
Purpose of the Study:
- To develop and test a quantum entropy (SQuniv) for pure states in system-environment interactions.
- To formulate microcanonical entropy using a quantum microcanonical shell concept.
- To investigate the validity of the classical relation TΔS = ΔF in the quantum realm.
Main Methods:
- Numerical simulations to test the quantum entropy formulation.
- Development of a quantum microcanonical shell model.
- Analysis of system-environment coupling effects on entropy.
Main Results:
- A quantum entropy (SQuniv) was successfully developed for realistic temperature baths.
- Numerical simulations confirmed "excess entropy production" (ΔSx) arising from quantum time-energy uncertainty.
- Excess entropy production decreases as system-environment coupling approaches zero.
Conclusions:
- The quantum microcanonical ensemble and universe entropy are well-founded concepts.
- These concepts provide a basis for studying time-dependent processes with significant excess entropy production.
- The findings bridge classical and quantum statistical mechanics for entropy.
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...
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.
01:18Entropy
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...
01:20Entropy 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...