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Classical and quantum thermodynamics described as a system-bath model: The dimensionless minimum work principle.
Shoki Koyanagi1, Yoshitaka Tanimura1
1Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.
The Journal of Chemical Physics
|June 21, 2024
Summary
This study develops a unified thermodynamic theory for classical and quantum systems using dimensionless potentials. It establishes conditions for thermodynamics validity in small systems and extends it to non-equilibrium processes.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Quantum Mechanics
Background:
- Classical and quantum systems require distinct thermodynamic descriptions.
- Extending thermodynamics to small and non-equilibrium systems remains a challenge.
Purpose of the Study:
- To formulate a unified thermodynamic theory applicable to both classical and quantum systems.
- To establish conditions for thermodynamic validity in small systems.
- To provide a basis for extending thermodynamics to non-equilibrium conditions.
Main Methods:
- Development of a dimensionless thermodynamic potential based on intensive and extensive variables.
- Application of dimensionless minimum work and maximum entropy principles.
- Numerical verification using quantum Fokker-Planck and Kramers equations for a Brownian system.
Main Results:
- Obtained Massieu-Planck potentials as entropic potentials and Helmholtz-Gibbs potentials as free energy.
- Demonstrated interconversion of potentials via time-dependent Legendre transformations.
- Validated the theory for anharmonic Brownian systems in classical and quantum regimes.
Conclusions:
- The proposed thermodynamic theory is applicable to both classical and quantum systems.
- Conditions for the validity of thermodynamics in small, Hamiltonian-described systems are clarified.
- A foundation is laid for extending thermodynamic principles to non-equilibrium scenarios.
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