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Second Law of Thermodynamics without Einstein Relation
Benjamin Sorkin1, Haim Diamant1, Gil Ariel2
1Tel Aviv University, School of Chemistry and Center for Physics and Chemistry of Living Systems, 69978 Tel Aviv, Israel.
Physical Review Letters
|January 29, 2025
Summary
Active systems violate the Einstein relation, breaking connections between entropy and heat. A new temperature-like variable restores these thermodynamic laws for non-equilibrium systems.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Active Matter Physics
Background:
- Active and living systems are driven out of thermodynamic equilibrium.
- These systems often violate the Einstein relation due to active particle fluctuations.
- This violation disconnects particle fluctuations from medium dissipation.
Purpose of the Study:
- To investigate the breakdown of the Einstein relation in non-equilibrium systems.
- To analyze the consequences for thermodynamic relations, including fluctuation theorems.
- To propose a method for restoring thermodynamic consistency in active systems.
Main Methods:
- Theoretical analysis of active systems driven out of equilibrium.
- Examination of the relationship between informatic entropy production and heat dissipation.
- Development of a temperature-like variable to reconcile thermodynamic quantities.
Main Results:
- The widely used relation between informatic entropy production and heat dissipation does not hold in active systems.
- Fluctuation theorems for mechanical work, such as Jarzynski and Crooks theorems, are invalidated.
- A temperature-like variable is proposed that restores the correspondence and generalizes the second law of thermodynamics.
Conclusions:
- Departure from the fluctuation-dissipation theorem underlies the breakdown of thermodynamic relations in active systems.
- The proposed temperature-like variable ensures non-negative dissipated heat, vanishing at equilibrium.
- The Clausius inequality, Carnot efficiency, and extractable work relations are recovered, extending their validity to active systems.
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