Thermodynamics of Micro- and Nano-Systems Driven by Periodic Temperature Variations
By Kay Brandner, Keiji Saito, U. Seifert. 2015
147 citations recorded by the source corpus.
We introduce a general framework for analyzing the thermodynamics of small systems that are driven by both a periodic temperature variation and some external parameter modulating their energy. This set-up covers, in particular, periodic micro and nano-heat engines. In a first step, we show how to express total entropy production by properly identified time-independent affinities and currents without making a linear response assumption. In linear response, kinetic coefficients akin to Onsager coefficients can be identified. Specializing to a Fokker-Planck type dynamics, we show that these coefficients can be expressed as a sum of an adiabatic contribution and one reminiscent of a Green-Kubo expression that contains deviations from adiabaticity. Furthermore, we show that the generalized kinetic coefficients fulfill an Onsager-Casimir type symmetry tracing back to microscopic reversibility. This symmetry allows for non-identical off-diagonal coefficients if the driving protocols are not symmetric under time-reversal. We then derive a novel constraint on the kinetic coefficients that is sharper than the second law and provides an efficiency-dependent bound on power. As one consequence, we can prove that the power vanishes at least linearly when approaching Carnot efficiency. We illustrate our general framework by explicitly working out the paradigmatic case of a Brownian heat engine realized by a colloidal particle in a time-dependent harmonic trap subject to a periodic temperature profile. This case study reveals inter alia that our new general bound on power is asymptotically tight.
Subfields: Condensed Matter Physics, Mechanics of Materials, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/3d3d57ea54c93ba2933e6ba7d9fd2acb37f97234
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In Statistical and Nonlinear Physics
Citations in the corpus
- Current fluctuations and transport efficiency for general Langevin systems (2017, background): “In this case, we define the heat exchange with the hot and cold bath analog to the definition for a timedependent temperature in [33], 〈Q̇h〉 = − 1 γ ∫ L”
- Fundamental aspects of steady-state conversion of heat to work at the nanoscale (2016, background): “[498] and discuss the linear response structure by using a general stochastic approach.”