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Equilibrium Conditions for a Particle01:23

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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.
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Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so...
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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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A rigid body is said to be in dynamic equilibrium when both its linear and angular acceleration are zero, relative to an inertial frame of reference. This means that a body in equilibrium can be moving, but only when its linear and angular velocities are constant. A rigid body is said to be in static equilibrium when it is at rest in the selected frame of reference. The distinction between static equilibrium (e.g., a state of rest) and dynamic equilibrium (e.g, a state of uniform motion) is...
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Static equilibrium is a special case in mechanics that is very important in everyday life. It occurs when the net force and the net torque on an object or system are both zero. This means that both the linear and angular accelerations are zero. Thus, the object is at rest, or its center of mass is moving at a constant velocity. However, this does not mean that no forces are acting on the object within the system. In fact, there are very few scenarios on Earth in which no forces are acting upon...
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Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
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How Far from Equilibrium Is Active Matter?

Étienne Fodor1, Cesare Nardini2,3, Michael E Cates2,3

  • 1Université Paris Diderot, Sorbonne Paris Cité, MSC, UMR 7057 CNRS, 75205 Paris, France.

Physical Review Letters
|July 30, 2016
PubMed
Summary
This summary is machine-generated.

Active matter systems, driven out of equilibrium, exhibit time-reversal symmetry at short persistence times. This finding reveals an effective fluctuation-dissipation theorem, offering new insights into non-equilibrium dynamics.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Soft Matter

Background:

  • Active matter systems lack a generalized Stokes-Einstein relation, driving them out of thermal equilibrium.
  • Understanding the microscopic energy injection and dissipation is key to characterizing these systems.

Purpose of the Study:

  • To investigate the dynamics of active matter systems with persistent noises.
  • To determine if time-reversal symmetry is maintained at small but finite persistence times.
  • To explore the implications for fluctuation-dissipation theorems in non-equilibrium systems.

Main Methods:

  • Perturbative computation of the steady-state measure for interacting particles.
  • Analysis of entropy production rate at short persistence times.
  • Modeling systems with viscous drags and correlated noises.

Main Results:

  • Active matter systems with short persistence times exhibit time-reversal symmetry.
  • The entropy production rate vanishes for short persistent times.
  • An effective fluctuation-dissipation theorem emerges, similar to equilibrium systems.

Conclusions:

  • Non-conservative forces drive active systems out of equilibrium, even when interacting with a viscoelastic bath.
  • The study provides energetic insights into the departure of active systems from equilibrium.
  • The findings suggest a unified framework for understanding equilibrium and non-equilibrium statistical mechanics.