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Work relations for time-dependent states
Naoko Nakagawa1, Shin-ichi Sasa
1College of Science, Ibaraki University, Mito, Ibaraki 310-8512, Japan.
Summary
Researchers derived a new formula connecting generalized free energy and thermodynamic work for time-dependent systems. This extends previous findings to include momentum, using a symmetric entropy measure.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Non-equilibrium Systems
Background:
- Generalized free energy is defined using relative entropy for time-dependent states.
- Sivak and Crooks previously linked generalized free energy to thermodynamic work in overdamped systems.
Purpose of the Study:
- To rederive and generalize the relation between generalized free energy and thermodynamic work.
- To extend the applicability to systems with momentum degrees of freedom.
Main Methods:
- Re-derivation of the Sivak-Crooks relation.
- Connection to extended Clausius relation in steady-state thermodynamics.
- Generalization using symmetric entropy for systems with momentum.
Main Results:
- A generalized relation is established for systems with momentum degrees of freedom.
- The Shannon entropy in generalized free energy is replaced by a symmetric entropy.
- The work-thermodynamics connection is extended beyond overdamped systems.
Conclusions:
- The derived relation provides a broader understanding of thermodynamic work in non-equilibrium systems.
- The generalization is crucial for systems involving kinetic energy or momentum.
- This work bridges concepts from steady-state and time-dependent thermodynamics.
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