Sustaining a temperature difference
Sustaining a temperature difference
We derive an expression for the minimal rate of entropy that sustains two reservoirs at different temperatures T_0 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>T</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> and T_\ell <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>T</mml:mi><mml:mi>ℓ</mml:mi></mml:msub></mml:math> . The law displays an intuitive \ell^{-1} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>ℓ</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math> dependency on the relative distance and a characterisic \log^2 (T_\ell/T_0) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mo>log</mml:mo><mml:mn>2</mml:mn></mml:msup><mml:mo stretchy="false" …