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1.
We explain the (non-)validity of close-to-equilibrium entropy production principles in the context of linear electrical circuits.
Both the minimum and the maximum entropy production principles are understood within dynamical fluctuation theory. The starting
point are Langevin equations obtained by combining Kirchoff’s laws with a Johnson-Nyquist noise at each dissipative element
in the circuit. The main observation is that the fluctuation functional for time averages, that can be read off from the path-space
action, is in first order around equilibrium given by an entropy production rate.
That allows to understand beyond the schemes of irreversible thermodynamics (1) the validity of the least dissipation, the
minimum entropy production, and the maximum entropy production principles close to equilibrium; (2) the role of the observables’
parity under time-reversal and, in particular, the origin of Landauer’s counterexample (1975) from the fact that the fluctuating
observable there is odd under time-reversal; (3) the critical remark of Jaynes (1980) concerning the apparent inappropriateness
of entropy production principles in temperature-inhomogeneous circuits. 相似文献
2.
We discuss the transient and steady state fluctuation relation for a mechanical system in contact with two deterministic thermostats
at different temperatures. The system is a modified Lorentz gas in which the fixed scatterers exchange energy with the gas
of particles, and the thermostats are modelled by two Nosé-Hoover thermostats applied at the boundaries of the system. The
transient fluctuation relation, which holds only for a precise choice of the initial ensemble, is verified at all times, as
expected. Times longer than the mesoscopic scale, needed for local equilibrium to be settled, are required if a different
initial ensemble is considered. This shows how the transient fluctuation relation asymptotically leads to the steady state
relation when, as explicitly checked in our systems, the condition found in (D.J. Searles, et al., J. Stat. Phys. 128:1337,
2007), for the validity of the steady state fluctuation relation, is verified. For the steady state fluctuations of the phase
space contraction rate Λ and of the dissipation function Ω, a similar relaxation regime at shorter averaging times is found.
The quantity Ω satisfies with good accuracy the fluctuation relation for times larger than the mesoscopic time scale; the
quantity Λ appears to begin a monotonic convergence after such times. This is consistent with the fact that Ω and Λ differ
by a total time derivative, and that the tails of the probability distribution function of Λ are Gaussian. 相似文献