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Finite-time fluctuation theorem for oscillatory lattices driven by a temperature gradient
1Department of Physics and Jiujiang Research Institute, Xiamen University, Xiamen 361005, China.
Physical Review. E
|July 17, 2021
Summary
The total entropy production in a FPUT-β chain does not satisfy fluctuation relations over finite times due to broken time-reversal symmetry. Medium entropy production, however, approaches steady-state fluctuation theorems with increasing time.
Area of Science:
- Statistical Mechanics
- Non-equilibrium Thermodynamics
- Condensed Matter Physics
Background:
- The fluctuation theorem (FT) provides insights into non-equilibrium systems.
- Understanding entropy production in finite-time processes is crucial for complex systems.
- The Fermi-Pasta-Ulam-Tsingou-β (FPUT-β) chain is a standard model for studying nonlinear dynamics and heat transport.
Purpose of the Study:
- To investigate the finite-time fluctuation theorem for master functional, total entropy production, and medium entropy.
- To analyze the behavior of these quantities in a one-dimensional FPUT-β chain coupled to heat reservoirs.
- To determine the conditions under which steady-state fluctuation theorems are satisfied.
Main Methods:
- Numerical simulations of the one-dimensional FPUT-β chain.
- Theoretical analysis of entropy production and fluctuation relations.
- Investigation of time-reversal symmetry in non-equilibrium steady states.
Main Results:
- The non-equilibrium steady-state distribution of the FPUT-β chain violates time-reversal symmetry.
- Total entropy production does not satisfy the fluctuation relation for finite times.
- Medium entropy production approaches the conventional steady-state fluctuation theorem (SSFT) in the infinite time limit.
- Medium entropy production rate exhibits nonmonotonic dependence on anharmonicity due to phonon transport competition.
Conclusions:
- Finite-time fluctuation relations are violated for total entropy production in the studied FPUT-β chain.
- Generalized SSFT for medium entropy monotonically converges to the conventional SSFT with increasing time.
- The nonmonotonic behavior of medium entropy production and SSFT differences highlights complex interplay of anharmonicity and phonon transport.
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