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Entropy02:39

Entropy

38.1K
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...
38.1K
Entropy01:18

Entropy

3.8K
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...
3.8K
The Entropy as a State Function01:14

The Entropy as a State Function

104
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...
104
Third Law of Thermodynamics02:38

Third Law of Thermodynamics

23.3K
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.
23.3K
Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

5.3K
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...
5.3K
Entropy and the Second Law of Thermodynamics01:26

Entropy and the Second Law of Thermodynamics

274
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...
274

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Rigorous Excited-State Entropy in Finite-Temperature Time-Dependent Density Functional Theory.

T A Niehaus1

  • 1Institut Lumière Matière, CNRS UMR5306, Université Lyon 1, Université de Lyon, 69622 Villeurbanne CEDEX, France.

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|April 6, 2026
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Summary
This summary is machine-generated.

This study introduces a new method for calculating excited-state properties at finite temperatures using Time-Dependent Density Functional Theory (TDDFT). The approach improves descriptions of molecular behavior by considering the full density matrix, crucial for warm dense matter.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Materials Science

Background:

  • Accurate modeling of excited-state properties is essential for understanding chemical reactions and material behavior.
  • Existing methods often simplify excited-state occupation numbers, limiting their applicability at finite temperatures.
  • Finite electronic temperatures introduce complexities like fractional occupations that challenge traditional theoretical frameworks.

Purpose of the Study:

  • To develop a formal derivation of the excited-state difference density matrix at finite electronic temperatures.
  • To incorporate full density matrix and orbital relaxations into Time-Dependent Density Functional Theory (TDDFT) calculations.
  • To provide a more rigorous theoretical framework for excited states in systems with significant fractional occupations.

Main Methods:

  • Formal derivation of the excited-state difference density matrix.
  • Utilizing the Z-vector formalism to include orbital relaxations.
  • Implementation within the Time-Dependent Density Functional Tight-Binding (TD-DFTB) framework.
  • Application to torsional rotation of ethylene and charge transfer in p-nitroaniline.

Main Results:

  • The developed method successfully incorporates the full density matrix and orbital relaxations.
  • Application to ethylene and p-nitroaniline demonstrates the method's capability.
  • Defining excited-state entropy via the full density matrix improves potential energy surface descriptions.

Conclusions:

  • The new TDDFT framework offers a rigorous approach to excited states at finite temperatures.
  • This method enhances the description of systems with fractional occupations, such as warm dense matter.
  • The findings pave the way for more accurate simulations in complex physical and chemical systems.