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Related Concept Videos

Classical Mechanics01:12

Classical Mechanics

Classical mechanics provides a mathematical description of the motion of bodies under the influence of forces. A key principle within this field is the work-energy theorem, which establishes a bridge between the net work done on an object and its kinetic energy.The work-energy theorem states that the net work done on a particle by all the forces acting on it equals the change in its kinetic energy.In simple terms, the work-energy theorem is a method to analyze the effects of forces on an...
Classification of Systems-I01:26

Classification of Systems-I

Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
Principle of Virtual Work: Problem Solving01:13

Principle of Virtual Work: Problem Solving

The principle of virtual work is an essential concept in the field of mechanics and engineering. This is used to solve problems related to the equilibrium of a structure or system. It is based on the assumption that if a system is in equilibrium, the work done by all the forces during a virtual displacement is zero. This principle is applied by considering virtual displacements of the system and the corresponding work done by internal and external forces.
To apply the principle of virtual work,...
Second Order systems II01:18

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If  ζ...
Limits of the First Law of Thermodynamics01:22

Limits of the First Law of Thermodynamics

Spontaneous processes, like a rock falling to the ground or sodium reacting with chlorine, occur without external work and often involve a decrease in the system‘s energy. However, certain endothermic processes, such as the dissolution of sodium chloride in water, occur spontaneously even though they increase the energy of the system. This limitation suggests that the First Law of Thermodynamics, which states that the total energy of a system is constant in an isolated system, cannot fully...
Second Order systems I01:20

Second Order systems I

A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...

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Related Experiment Video

Updated: Jul 13, 2026

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Minimal-work principle and its limits for classical systems.

A E Allahverdyan1, Th M Nieuwenhuizen

  • 1Yerevan Physics Institute, Alikhanian Brothers St 2, Yerevan, Armenia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 7, 2007
PubMed
Summary

The minimal-work principle states that work done on isolated systems is minimized during slow, adiabatic processes. This study confirms its validity in classical mechanics for ergodic systems, exploring limitations in non-ergodic cases.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Classical Mechanics

Background:

  • The minimal-work principle, a facet of the second law of thermodynamics, posits minimal work for adiabatic processes in isolated systems.
  • It is operationally defined for finite, few-particle Hamiltonian systems.

Purpose of the Study:

  • To investigate the validity of the minimal-work principle within classical Hamiltonian mechanics.
  • To identify conditions and system types for which the principle holds or fails.

Main Methods:

  • Analysis within the framework of classical Hamiltonian mechanics.
  • Examination of work as an observable in relation to system ergodicity.
  • Theoretical exploration of ergodic and non-ergodic systems.

Main Results:

  • The minimal-work principle is validated for systems where work is an ergodic function.
  • The principle's applicability to non-ergodic systems is shown to be conditional.
  • Examples illustrating the principle's boundaries and potential experimental realizations are provided.

Conclusions:

  • The ergodicity of the work observable is a key factor in the validity of the minimal-work principle in classical mechanics.
  • Understanding system ergodicity is crucial for applying and extending the minimal-work principle.
  • The findings offer insights into the fundamental limits of work in thermodynamic processes.