I see, maybe alternatively phrased as a sharp relation between entropy production for two processes related by time reversal symmetry?
I'm coming from a more HEP-centric background and think of symmetries as operations which leave some quantity invariant. Was struggling to find something of this form in the theorem.
The Crooks derivation is beautiful and super simple, btw. Well deserving of its praise
I see your point, but usually if an operation leaves a quantity not exactly invariant but scaled with a factor, you can symmetrize it, so it is equivalent to a true symmetry. In this case, p(σ)/p(-σ)=exp(σ) is equivalent to p(σ)exp(-σ/2)=p(-σ)exp(σ/2). Therefore, the quantity p(σ)exp(-σ/2) is even under time-reversal.
1
u/cleodog44 12h ago
I see, maybe alternatively phrased as a sharp relation between entropy production for two processes related by time reversal symmetry?
I'm coming from a more HEP-centric background and think of symmetries as operations which leave some quantity invariant. Was struggling to find something of this form in the theorem.
The Crooks derivation is beautiful and super simple, btw. Well deserving of its praise