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Work and heat are fundamental concepts in thermodynamics, denoting the transfer of energy. Work is the energy transferred due to the movement of an object under force, represented as the dot product of the force and displacement vectors. An example can be seen in a gas confined by a frictionless piston. The gas performs work on its surroundings when the piston moves outward, reducing the system's energy.This infinitesimal amount of work (dw) performed by the system against a constant external...

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Fluctuation symmetries for work and heat.

Marco Baiesi¹, Tim Jacobs, Christian Maes

¹Instituut voor Theoretische Fysica, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 10, 2006

Summary

This study examines a particle in a medium using a Langevin equation. It identifies conditions for exact work fluctuation symmetry and discusses corrections to heat fluctuation theorems.

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Area of Science:

Statistical Mechanics
Non-equilibrium Thermodynamics
Physical Chemistry

Background:

The Langevin equation describes particle dynamics in a medium, influenced by random forces and friction.
Fluctuation theorems in non-equilibrium systems relate work and heat under specific conditions.

Purpose of the Study:

To investigate the conditions under which fluctuations of dissipative work satisfy an exact symmetry.
To analyze the validity of fluctuation theorems for dissipated heat, considering temporal boundary effects.

Main Methods:

Utilizing a Langevin equation with a time-dependent potential driven by an external protocol.
Deriving and analyzing the fluctuation theorems for dissipative work and heat.

Main Results:

Identified specific conditions on the potential and external protocol for exact work fluctuation symmetry.
Presented counterexamples where these conditions are not met, violating the standard fluctuation theorem.
Derived a corrected fluctuation relation for dissipated heat, accounting for temporal boundary terms, which holds generally.

Conclusions:

The study provides precise conditions for the validity of work fluctuation theorems in driven systems.
A generalized fluctuation relation for dissipated heat is established, addressing limitations of standard theorems.