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In a thermal conduction context and according to this formula : $\varphi=\frac{\Delta T}{R_{th}}$, the heat transfer is proportional to the temperature gradient.

How does one physically explain the mecanism leading to that ? (At a microscopic pov maybe).

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  • $\begingroup$ Think about a stick with two different temperatures at either end. What does temperature signify to you at a microscopic poy and think about what would be the situation of the atoms/molecules of the stick at either end. Also I think it is the rate of heat transfer and not heat transfer that is proportional to the temperature gradient....right ;) $\endgroup$
    – Ghosal_C
    Commented May 6, 2017 at 1:02
  • $\begingroup$ None of the answers address the proportionality, only the direction of flow, although I think that was the question. Could be wrong $\endgroup$
    – James Well
    Commented May 28, 2022 at 23:21

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Just like water is flowing faster if a river is steeper most fluxes are proportional to some sort of gradient.

In your example it's a gradient in entropy, which can be thought of as a measure of order in a system. The system is trying to overcome the temperature difference in different regions which causes a heatflow, which is stronger the further the system is from equilibrium.

A nice example where you can see that a gradient in entropy does produce a measurable entropic force are polymers. https://en.wikipedia.org/wiki/Ideal_chain

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A rough outline: If particles move "double as violent" (which is called temperature), they bump double as much into neighbours thus passing double as much energy to that neighbour (which is called heat conduction).

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