Related Experiment Video
Updated: Jun 14, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Approach to thermal equilibrium of macroscopic quantum systems.
Sheldon Goldstein1, Joel L Lebowitz, Christian Mastrodonato
1Departments of Mathematics and Physics, Rutgers University, Piscataway, New Jersey 08854-8019, USA. oldstein@math.rutgers.edu
Summary
Isolated macroscopic quantum systems reach thermal equilibrium for most times. This occurs for typical Hamiltonians, aligning with the quantum ergodic theorem.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Quantum thermodynamics
Background:
- Macroscopic quantum systems are studied in isolation.
- Thermal equilibrium is defined by a subspace of energy eigenstates.
- A system is in thermal equilibrium if its state vector is close to this subspace.
Purpose of the Study:
- To investigate the thermalization of isolated macroscopic quantum systems.
- To demonstrate that typical quantum systems evolve into a thermal equilibrium state.
Main Methods:
- Consideration of a microcanonical energy shell (H) within the system's Hilbert space.
- Definition of a thermal equilibrium macrostate (H(eq)) as a large subspace of H.
- Analysis of the time evolution of an initial state vector (psi(0)).
Main Results:
- For typical Hamiltonians, initial state vectors evolve to be in thermal equilibrium for most times.
- The dimension of the equilibrium subspace (H(eq)) is close to the total dimension of the energy shell (H).
- This dynamical thermalization is a general property of isolated quantum systems.
Conclusions:
- Isolated macroscopic quantum systems naturally evolve towards thermal equilibrium.
- The findings support the quantum ergodic theorem, explaining thermalization from first principles.
- This work provides a foundation for understanding thermalization in quantum statistical mechanics.
Related Concept Videos
01:14The Zeroth Law of Thermodynamics
Systems in mechanical equilibrium exert equal pressure on the separating wall. Similarly, systems in thermal equilibrium share a common thermodynamic property: temperature.Temperature is a measure of the average kinetic energy of particles within a system. More generally, it reflects the internal energy state of the system. The higher the temperature, the more energy a system has, given that other variables, such as volume and pressure, remain constant. However, temperature is not a form of...
01:11Temperature and Thermal Equilibrium
Heat and temperature are essential concepts for everyone every day. The study of heat and temperature is part of an area of physics known as thermodynamics. It is not always easy to distinguish heat and temperature.
The concept of temperature has evolved from the common concepts of hot and cold. The scientific definition of temperature explains more than just our sense of hot and cold. Temperature is operationally defined as the quantity measured with a thermometer. Furthermore, temperature is...
The concept of temperature has evolved from the common concepts of hot and cold. The scientific definition of temperature explains more than just our sense of hot and cold. Temperature is operationally defined as the quantity measured with a thermometer. Furthermore, temperature is...
01:06Thermodynamic Systems
A thermodynamic system is a set of objects whose thermodynamic properties are of interest. The system is considered to be embedded in its surroundings or the environment. The system and its environment can exchange heat and do work on each other through a boundary that separates them. However, the immediate surroundings of the system interact with it directly and therefore have a much stronger influence on its behavior and properties.
Consider an example of tea boiling in a kettle. The tea and...
Consider an example of tea boiling in a kettle. The tea and...
01:14Zeroth Law of Thermodynamics
Experimentally, if object A is in equilibrium with object B, and object B is in equilibrium with object C, then object A is in equilibrium with object C. That statement of transitivity is called the "zeroth law of thermodynamics." For example, a cold metal block and a hot metal block are both placed on a metal plate at room temperature. Eventually, the cold block and the plate will be in thermal equilibrium. In addition, the hot block and the plate will be in thermal equilibrium. By the zeroth...
02:49Second Law of Thermodynamics
In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...
00:53Second Law of Thermodynamics
The Second Law of Thermodynamics states that entropy, or the amount of disorder in a system, increases each time energy is transferred or transformed. Each energy transfer results in a certain amount of energy that is lost—usually in the form of heat—that increases the disorder of the surroundings. This can also be demonstrated in a classic food web. Herbivores harvest chemical energy from plants and release heat and carbon dioxide into the environment. Carnivores harvest the chemical energy...