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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
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Experimentally, if object A is in equilibrium with object B, and object B is in equilibrium with object C, then object A is in equilibrium with object C. That statement of transitivity is called the "zeroth law of thermodynamics." For example, a cold metal block and a hot metal block are both placed on a metal plate at room temperature. Eventually, the cold block and the plate will be in thermal equilibrium. In addition, the hot block and the plate will be in thermal equilibrium.
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Second Law of Thermodynamics without Einstein Relation.

Benjamin Sorkin1, Haim Diamant1, Gil Ariel2

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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.

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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.