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A Computational Modeling Approach to Investigate the Influence of Hyperthermia on the Tumor Microenvironment

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Nonequilibrium work relations for systems subject to mechanical and thermal changes.

Riccardo Chelli¹

¹Dipartimento di Chimica, Università di Firenze, Via della Lastruccia 3, I-50019 Sesto Fiorentino, Italy. chelli@chim.unifi.it

The Journal of Chemical Physics

|February 12, 2009

Summary

This study generalizes the Crooks fluctuation theorem for Hamiltonian and non-Hamiltonian systems undergoing mechanical and thermal changes. It extends nonequilibrium work relations, offering a unified framework for statistical mechanics research.

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Area of Science:

Statistical Mechanics
Non-equilibrium Thermodynamics
Physical Chemistry

Background:

The Crooks fluctuation theorem is crucial for understanding non-equilibrium processes.
Existing formulations often focus on specific system types (e.g., Hamiltonian).
A generalized approach is needed to encompass broader physical systems.

Purpose of the Study:

To derive generalized forms of the Crooks fluctuation theorem.
To extend its applicability to both Hamiltonian and non-Hamiltonian systems.
To unify derivations for mechanical and thermal changes.

Main Methods:

Derivations based on the Liouville equation.
Assumption of stationary probability distribution for fixed parameters and temperature.
Application to systems with isochoric-isokinetic and isothermal-isobaric equations of motion.

Main Results:

Generalized Crooks fluctuation theorem derived for diverse systems.
Identical derivations for Hamiltonian and non-Hamiltonian cases.
Extended several key non-equilibrium work relations (Jarzynski equality, Bennett acceptance ratio, etc.).

Conclusions:

The generalized theorem provides a unified framework for non-equilibrium statistical mechanics.
The methodology is broadly applicable and extends to other work theorems.
Demonstrates applicability through illustrative examples in thermodynamics.