Second Law of Thermodynamics without Einstein Relation
arxiv(2024)
摘要
Materials that are constantly driven out of thermodynamic equilibrium, such
as active and living systems, typically violate the Einstein relation. This may
arise from active contributions to particle fluctuations which are unrelated to
the dissipative resistance of the surrounding medium. We show that in these
cases the widely used relation between informatic entropy production and heat
dissipation does not hold. Consequently, fluctuation relations for the
mechanical work, such as the Jarzynski and Crooks theorems, are invalid. We
relate the breaking of the correspondence between entropy production and heat
dissipation to the breaking of the fluctuation-dissipation theorem. We propose
a temperature-like variable which restores this correspondence and gives rise
to a generalized second law of thermodynamics, whereby the dissipated heat is
necessarily nonnegative and vanishes at equilibrium. The Clausius inequality,
Carnot maximum efficiency theorem, and relation between the maximum extractable
work and the change of free energy are recovered as well.
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