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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Finite bath fluctuation theorem.

Michele Campisi¹, Peter Talkner, Peter Hänggi

¹Institute of Physics, University of Augsburg, Universitätsstrasse 1, D-86153 Augsburg, Germany. michele.campisi@physik.uni-augsburg.de

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

|November 13, 2009

Summary

This summary is machine-generated.

A finite bath fluctuation theorem, applicable to systems thermalized with baths of finite specific heat, was demonstrated. This generalized theorem encompasses both canonical and microcanonical fluctuation theorems as limiting cases.

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Area of Science:

Statistical mechanics
Thermodynamics
Non-equilibrium systems

Background:

Fluctuation theorems provide insights into the statistical properties of work and entropy production in non-equilibrium processes.
The Crooks fluctuation theorem is a key result relating forward and reverse processes in stochastic thermodynamics.
Existing fluctuation theorems often assume specific properties of the thermal bath, such as infinite or vanishing specific heat.

Purpose of the Study:

To demonstrate the validity of a finite bath fluctuation theorem of the Crooks type.
To show that this generalized theorem unifies existing canonical and microcanonical fluctuation theorems.
To provide a theoretical framework applicable to systems interacting with finite heat baths.

Main Methods:

Derivation of a generalized fluctuation theorem for systems coupled to a bath with finite, energy-independent specific heat.
Analysis of the limiting cases of infinite and vanishing bath specific heat.
Application of the theorem to a model system of hard disks in a rectangular box.

Main Results:

A finite bath fluctuation theorem of the Crooks type is shown to hold for systems thermalized via weak coupling to a bath with finite specific heat.
The derived theorem correctly reduces to the canonical fluctuation theorem for infinite bath specific heat.
The theorem also reduces to the microcanonical fluctuation theorem for vanishing bath specific heat.

Conclusions:

The finite bath fluctuation theorem offers a more general description of non-equilibrium thermodynamics.
This work unifies previously distinct fluctuation theorems under a single, more comprehensive framework.
The findings are illustrated by a physically relevant model, demonstrating the theorem's applicability.