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When two bodies A and B are in thermal equilibrium, I wonder if the entropies of A and B stop changing (ie. stay constant), or their entropies still change but the net change is zero.

What I mean for the latter is that the entropy of body A increases after it receives heat from body B, but after it gives the same amount of heat back to body B, its entropy decreases. The net change in entropy in body A is zero?

Qmechanic
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John Davies
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    In an equilibrium the macroscopic parameters, including entropy, by definition do not change. – hyportnex Apr 03 '23 at 01:30
  • @hyportnex I think you are referring to entropy of universe. At thermal equilibrium, rates of change of entropy of A and B are equal, so entropies of A and B still changes but net change is zero. – John Davies Apr 03 '23 at 01:50
  • OK, then what is your definition of equilibrium? – hyportnex Apr 03 '23 at 01:54
  • @hyportnex like I said, thermal equilibrium happens when the change of entropy of A equals to the change of entropy of B. – John Davies Apr 03 '23 at 02:25
  • In any Carnot cycle the entropy is conserved. During the higher temperature isothermal stage a certain amount of entropy, say $S_0$ is absorbed by the engine from the reservoir, then after adiabatic work it is unchanged and in the following lower temperature isothermal stage it is expelled in the lower temperature reservoir. The engine is not in equilibrium with its environment, instead it is either working or exchanging entropy so that the total entropy with the environment is constant. You are confusing a reversible process with equilibrium. – hyportnex Apr 03 '23 at 02:35
  • Please consider editing your question to provide more details. It's not clear what you mean when you mention thermal equilibrium and then describe the objects heating each other alternately in turn. This seesawing exchange of heat doesn't seem to match consensus physics. – Chemomechanics Apr 03 '23 at 04:08
  • I was thinking that if the temperature of body A is greater than the body B $T_A>T_B$, then heat will flow from A to B until thermal equilibrium is reached $T_A=T_B$. During thermal equilibrium, A and B exchange heat at equal rates but the net change in heat is zero. Wait, I get it now, If the net heat flow is zero, then there is no entropy increase, thus entropy stays constant... – John Davies Apr 03 '23 at 04:44
  • The confusion may lie with "net change in heat.". Heat itself is a net energy transfer driven by a temperature difference, so it doesn't make much sense to talk about a change in heat. Heat is not a substance within a body; this is the debunked theory of caloric. – Chemomechanics Apr 03 '23 at 04:53
  • @Chemomechanics are you claiming that there is no heat flow between objects in thermal equilibrium? – John Davies Apr 03 '23 at 05:34
  • In radiative heat transfer, for example, it makes sense to model the photons as carrying energy and entropy between bodies, and at thermal equilibrium, the amounts are equal and opposite. Is this what you're asking about? Your question is unclear, as it describes the bodies taking turns, which they don't do. Please consider clarifying. – Chemomechanics Apr 03 '23 at 06:54
  • See also Thermal equilibrium thermodynamics, Black body in thermal equilibrium, Question about thermal radiation and the 2nd Law. – Chemomechanics Apr 03 '23 at 07:14

2 Answers2

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Consider two systems adiabatically insulated from surrounding and are connected through eachother with a conducting wall and are at thermal equilibrium with temperature as $T_0$.

According to first law of thermodynamics $$dU=\sum_i F_i dx_i$$

Where $U$ is internal energy, $F_i$ are generalized force and $x_i$ are generalized displacement.

Since the two systems are insulated their combined energy cannot increase and since the temperature is $T_0$ which can be considered as generalized force with entropy as generalized displacement. If the temperature $T$ remains constant the entropy $S$ can't increase as $dU=0=Tds$.

Now coming to your question the thermodynamics or statistics in general deals with process over a large time average or through ensemble average, sure in small time limit there can be such processes where one system A gains energy and other system B loses (uncertainty). But at large times the overall effect must be zero.

Analogue of it is two frictionless (Analogue of adiabatically insulated) coupled harmonic oscillator sure they will oscillate (at some instances one oscillator will have more kinetic energy) but their means (energy etc.) will remain constant.

Pradyuman
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If heat flows from body B to body A, then entropy of A increases, while entropy of B decreases. The total entropy change, according to the second law of thermodynamics, is positive. Entropy does not conserve.

kludg
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