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Distribution of Molecular Speeds01:27

Distribution of Molecular Speeds

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The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a...
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First Law: Particles in One-dimensional Equilibrium01:10

First Law: Particles in One-dimensional Equilibrium

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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...
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First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

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Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about...
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Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

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Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
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Equilibrium Conditions for a Particle01:23

Equilibrium Conditions for a Particle

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When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
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Propagation Speed of Electromagnetic Waves01:30

Propagation Speed of Electromagnetic Waves

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Electromagnetic waves are consistent with Ampere's law. Assuming there is no conduction current Ampere's law is given as:
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Related Experiment Video

Updated: Jul 16, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Speed limits and locality in many-body quantum dynamics.

Chi-Fang Anthony Chen1, Andrew Lucas2, Chao Yin2

  • 1Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125, United States of America.

Reports on Progress in Physics. Physical Society (Great Britain)
|September 18, 2023
PubMed
Summary

This review explores mathematical speed limits for quantum information processing in many-body systems. It highlights advancements in applying Lieb-Robinson bounds to quantum computing and entanglement, while also discussing open questions.

Keywords:
Lieb–Robinson boundlocalitymathematical physicsquantum dynamicsquantum entanglement

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Mathematical Physics

Background:

  • The Lieb-Robinson Theorem, established in 1972, provides fundamental bounds on the speed of information propagation in quantum systems.
  • Recent decades have seen significant advancements in applying these bounds to diverse areas of quantum information processing.

Purpose of the Study:

  • To provide a comprehensive review of the mathematical speed limits on quantum information processing in many-body systems.
  • To highlight key developments, techniques, and outstanding questions in the field.
  • To offer self-contained proofs of essential results for newcomers.

Main Methods:

  • Review of theoretical advancements and applications of Lieb-Robinson bounds.
  • Analysis of extensions to systems with power-law interactions and interacting bosons.
  • Exploration of proofs for notions of locality in quantum gravity models.

Main Results:

  • Lieb-Robinson bounds are crucial for understanding quantum system simulatability on classical and quantum computers.
  • These bounds have been extended to address complex systems and demonstrate speed limits.
  • Applications include entanglement generation and characterization of ground states in gapped systems.

Conclusions:

  • The review consolidates progress in understanding quantum information speed limits.
  • It identifies promising research directions and open problems.
  • The provided proofs aim to facilitate entry for new researchers into this domain.