Negative entropy production rates in Drude-Sommerfeld metals

Abstract

It is commonly accepted that in typical situations the rate of entropy production is non-negative. We show that this assertion is not entirely correct, not even in the linear regime, if a time-dependent, external perturbation is not compensated by a rapid enough decay of the response function. This is demonstrated for three variants of the Drude model to describe electrical conduction in noble metals, namely the classical free electron gas, the Drude-Sommerfeld model, and the extended Drude-Sommerfeld model. The analysis is concluded with a discussion of potential experimental verifications and ramifications of negative entropy production rates.

Fluctuation theorem for irreversible entropy production in electrical conduction

“…As discussed in Ref. [5], negative values of Σ persist within a small vicinity of ω 0 t = nπ, n = 1, 2, 3, . .…”

“…The natural question arises, whether the two paradigms are consistent with each other, or rather whether the two "versions" of entropy production are equivalent. In particular, the occurrence of negative rates in irreversible thermodynamics [5,6,14] appears incompatible with the strict positivity of the stochastic entropy production rate often discussed in the literature [19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”

“…Interestingly, negative entropy production rates in open systems undergoing non-Markovian dynamics are somewhat commonplace [8][9][10][11][12]. However, our analysis is entirely based on the lag of response [13,41], which also gives rise to negative rates in Markovian settings [5,14].…”

“…Only recently, we showed in Ref. [5] that the entropy production in noble metals under AC driving exhibits non-monotonic growth as a function of time. In other words, in electrical conduction the entropy production rate can become negative.…”

Quantum Foundations of Classical Reversible Computing

“…It's worth noting that the entropy production rate can be negative in local systems due to non-Markovian dynamics[119] or systems with delayed response[120].Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 28 May 2021 doi:10.20944/preprints202105.0066.v3…”