## The Principle of MicroscopicReversibility

A fundamental of thermodynamics and chemistry which states that:

At equilibrium the rate of all forward reactions is equal to the rate of the corresponding back reactions.

For example, if A, B, and C are in a state of equilibrium in a test tube then the concentrations of A and of B and of C do not change - the composition of the mixture is unchanging with time, the essence of equilibrium. This might be because:

1. A reacts to give B, A -> B; B -> C; C -> A.
2. A -> B, B -> A; B -> C, C -> B.
The priciple says it cannot be case 1, and that, if it is case 2, the rate of A -> B is the same as the rate of B -> A and ditto for B and C.

#### Why Is the Principle Independent of the Second Law of Thermodynamics?

dU = T.dS - P.dV + μ.dN is the thermodynamic identity when the number of particles in the system is increased by an amount dN (only one type of particle is present for simplicity). (U internal energy, T temperature, S entropy, P pressure, V volume, μ chemical potential).

Imagine some gas is trapped in a blind ended cylinder fitted with a sliding piston. A force is applied to the piston and the piston slides in, compressing the gas, untill the force with which it pushes back on the piston is equal to the applied force. Then the motion stops. During the motion net entropy is produced, but when the forces balance and the piston stops moving no entropy is made - objects in mechanical contact do not produce entropy when they are at the same potential, P in this case.

It seems therefore that the Principle of Microscopic Reversibility is analagous to this and to the case where objects in thermal contact are at the same temperature. Abutting masses of fluid in a test tube, say, produce no entropy when they are at the same chemical potential. This implies there must exist a back reaction by analogy to the resistive force produced by the gas in the cylinder.

Thus the priciple is simply an analogy to objects in mechanical equlibrium and to objects in thermal equilibrium.

#### Reversible in its usual sense

Reversible is also being used in the usual thermodynamic sense to mean 'without losses or entropy creation'. Thus when the rate of back reaction equals the rate of the corresponding forward reaction no entropy is produced. This is analogous to two objects in thermal contact being at the same temperature or two objects in mechanical contact being at the same potential.

I think there exists a relationship connecting the entropy produced in a reaction and the ratio of the number of forward steps to backward steps of the forward and back reactions. This sounds wildly important but is, unfortunately, mysterious to Sporus.

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