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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.
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In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
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Related Experiment Video

Updated: Sep 11, 2025

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
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Force correlator for driven disordered systems at finite temperature.

Cathelijne Ter Burg1, Kay Jörg Wiese1

  • 1Laboratoire de Physique de l'Ećole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, 24 rue Lhomond, 75005 Paris, France.

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|August 19, 2025
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Summary
This summary is machine-generated.

This study numerically investigates the crossover between two critical points in disordered elastic systems. Researchers quantified how system behavior changes with varying temperature and driving velocity.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • Disordered elastic systems exhibit complex behavior when driven.
  • Pinning forces on the center of mass fluctuate, characterized by mean and variance.
  • Two well-understood fixed points exist: the depinning and zero-temperature equilibrium fixed points.

Purpose of the Study:

  • To numerically quantify the crossover between the depinning and zero-temperature equilibrium fixed points.
  • To explore the parameter space of driving velocity (v > 0) and temperature (T > 0).

Main Methods:

  • Utilized the functional renormalization group in the limit of vanishing temperature (T→0) and vanishing driving velocity (v→0).
  • Employed numerical methods to analyze the crossover in the T>0 and v>0 parameter space.

Main Results:

  • Characterized fluctuating pinning forces with mean f_{c}=-F_{w}[over ¯] and variance Δ(w)=F_{w}F_{0}[over ¯]^{c}.
  • Identified and analyzed deformations around the depinning and zero-temperature equilibrium fixed points.

Conclusions:

  • The study provides a numerical quantification of the crossover between distinct critical behaviors in disordered elastic systems.
  • Understanding this crossover is crucial for predicting system dynamics across various temperature and driving velocity regimes.