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Related Concept Videos

Phase Transitions02:31

Phase Transitions

Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to occupy...
Phase Transitions01:21

Phase Transitions

A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...
Phase Transitions: Vaporization and Condensation02:39

Phase Transitions: Vaporization and Condensation

The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules...
Phase Transitions: Sublimation and Deposition02:33

Phase Transitions: Sublimation and Deposition

Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...
Transition State Theory01:25

Transition State Theory

Transition-state theory, also known as activated-complex theory, provides a molecular-level explanation of reaction rates in both gas-phase and solution-phase reactions. It extends earlier kinetic models by considering the formation of a short-lived, high-energy configuration during a reaction.The progress of a chemical reaction can be represented using a reaction profile, which plots potential energy against the reaction coordinate. As two reactant molecules approach one another, their...
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.

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Related Experiment Video

Updated: Jul 2, 2026

Combining Microfluidics and Microrheology to Determine Rheological Properties of Soft Matter during Repeated Phase Transitions
11:38

Combining Microfluidics and Microrheology to Determine Rheological Properties of Soft Matter during Repeated Phase Transitions

Published on: April 19, 2018

The Riemann Hypothesis manifested in dynamical quantum phase transitions.

Shijie Wei1, Yue Zhai2,3, Quanfeng Lu4

  • 1Beijing Academy of Quantum Information Sciences, Beijing, China. weisj@baqis.ac.cn.

Nature Communications
|June 30, 2026
PubMed
Summary
This summary is machine-generated.

Researchers link the Riemann Hypothesis (RH) to quantum phase transitions. This discovery recasts the RH as a phase transition and suggests quantum computing can explore this mathematical problem.

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Last Updated: Jul 2, 2026

Combining Microfluidics and Microrheology to Determine Rheological Properties of Soft Matter during Repeated Phase Transitions
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Area of Science:

  • Quantum Physics
  • Number Theory
  • Condensed Matter Physics

Background:

  • The Riemann Hypothesis (RH) is a major unsolved problem in mathematics concerning the zeros of the Riemann zeta function.
  • Connecting mathematical concepts to physical phenomena can provide novel insights and verification methods.

Purpose of the Study:

  • To establish a direct correspondence between the nontrivial zeros of the Riemann zeta function and dynamical quantum phase transitions.
  • To explore the potential of quantum computing in investigating the Riemann Hypothesis.

Main Methods:

  • Engineering two complementary quantum many-body systems.
  • Characterizing these systems using the average accumulated phase factor and the Loschmidt amplitude.
  • Conducting a proof-of-principle experiment on a quantum processor.

Main Results:

  • A direct correspondence was established between Riemann zeta function zeros and quantum phase transitions.
  • The Riemann Hypothesis was recast as a phase transition occurring at a specific temperature.
  • A proof-of-principle experiment successfully demonstrated this correspondence.

Conclusions:

  • The study bridges nonequilibrium quantum dynamics and number theory.
  • Quantum computing offers a powerful platform for exploring the Riemann Hypothesis and other mathematical conjectures.
  • The identified transition mechanism provides a new perspective on the Riemann Hypothesis.