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Related Concept Videos

Entropy and the Second Law of Thermodynamics01:20

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

Entropy 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...
Entropy Change in Reversible Processes01:10

Entropy 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 Entropy as a State Function01:14

The 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...
Absolute Entropies and the Third Law of Thermodynamics01:23

Absolute 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...
First Law: Particles in One-dimensional Equilibrium01:10

First Law: Particles in One-dimensional Equilibrium

Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If we...

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Related Experiment Video

Updated: May 21, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

First principle nonlinear quantum dynamics using a correlation-based von Neumann entropy.

Till Westermann1, Uwe Manthe

  • 1Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, 33615 Bielefeld, Germany. till.westermann@uni-bielefeld.de

The Journal of Chemical Physics
|June 7, 2012
PubMed
Summary
This summary is machine-generated.

A new quantum dynamics concept uses correlation-based von Neumann entropy (CvN-entropy) to manage wavefunction complexity. This method offers improved accuracy and an intrinsic error estimate for complex systems.

Related Experiment Videos

Last Updated: May 21, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Area of Science:

  • Quantum dynamics
  • Computational chemistry
  • Theoretical physics

Background:

  • Established methods like multi-configurational time-dependent Hartree (MCTDH) face challenges in describing quantum dynamics in complex systems.
  • Wavefunction complexity can increase significantly over time, posing computational difficulties.
  • Accurate error estimation in quantum dynamics simulations is crucial but often requires knowledge of the exact solution.

Purpose of the Study:

  • To introduce a novel concept for describing quantum dynamics in complex systems.
  • To develop a method that constrains wavefunction complexity using correlation-based von Neumann entropy (CvN-entropy).
  • To derive and apply a generally applicable effective Hamiltonian for quantum dynamics.

Main Methods:

  • Extension of the Dirac-Frenkel variation principle.
  • Definition and application of a correlation-based von Neumann entropy (CvN-entropy) to measure wavefunction complexity.
  • Derivation of equations of motion using a CvN-entropy constraint, leading to an effective Hamiltonian with a nonlinear complexity-limiting operator.
  • Study of wave packet propagation on the diabatic B(2) potential energy surfaces of NO(2).

Main Results:

  • CvN-entropy increases significantly over time during standard wave packet propagation, irrespective of the coordinate system.
  • CvN-entropy constrained MCTDH propagation improves wavefunction accuracy on longer timescales, albeit with a slight compromise in short-time accuracy.
  • The loss of wavefunction norm is directly correlated with the overlap with the exact wavefunction, providing a built-in error estimate.

Conclusions:

  • The proposed CvN-entropy constrained approach offers a robust framework for managing wavefunction complexity in quantum dynamics.
  • The method provides an intrinsic error estimation without requiring knowledge of the exact wavefunction.
  • This approach enhances the accuracy and reliability of quantum dynamics simulations for complex systems.