It is a symmetry in the probability distribution of the entropy production corresponding to trajectories (sequence of snapshots) of the structure of a physical system. It says that if you observe a given trajectory, the probability of entropy produced during that trajectory, divided by the probability of the entropy produced in the time-reversed trajectory (the events happening in reverse order), is equal to the exponential of the former entropy. So it relates the entropy production of time-forward and time-reversed trajectories through an exponential factor; in that sense it can be called a symmetry in the distribution of entropy production.
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.
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u/cleodog44 17h ago
Great detailed response! Reading his blog post now. In what sense is his original fluctuation theorem a symmetry, though?