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A proof of Clausius' theorem for time reversible deterministic microscopic dynamics.

Denis J Evans¹, Stephen R Williams, Debra J Searles

¹Research School of Chemistry, Australian National University, Canberra, ACT 0200, Australia.

The Journal of Chemical Physics

|June 7, 2011

Summary

This study presents a new proof of the Clausius theorem, bypassing the need for the second law of thermodynamics. The findings are based on mechanics, causality, and recent fluctuation theorems.

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Area of Science:

Thermodynamics
Statistical Mechanics
Theoretical Physics

Background:

The Clausius theorem, a cornerstone of thermodynamics, was originally proven using the second law of thermodynamics.
A foundational proof of the Clausius theorem is essential for understanding thermodynamic principles.

Purpose of the Study:

To provide a novel proof of the Clausius theorem.
To demonstrate that the theorem can be derived without assuming the second law of thermodynamics.

Main Methods:

The proof utilizes fundamental laws of mechanics.
It incorporates a T-mixing property and an ergodic consistency condition.
The axiom of causality is a key component of the derivation.

Main Results:

A new, assumption-free proof of the Clausius theorem has been established.
The derivation relies on recently developed theorems, including the Evans-Searles and Crooks fluctuation theorems.
The proof also incorporates novel relaxation and dissipation theorems.

Conclusions:

The Clausius theorem can be derived from more fundamental principles than previously thought.
This work offers a new perspective on the foundations of thermodynamics.
The findings have implications for statistical mechanics and the understanding of irreversible processes.