Quantum entropy production as a measure of irreversibility

Abstract

We consider conservative quantum evolutions possibly interrupted by macroscopic measurements. When started in a nonequilibrium state, the resulting path-space measure is not time-reversal invariant and the weight of time-reversal breaking equals the exponential of the entropy production. The mean entropy production can then be expressed via a relative entropy on the level of histories. This gives a partial extension of the result for classical systems, that the entropy production is given by the source term of time-reversal breaking in the path-space measure.

Unified treatment of the quantum fluctuation theorem and the Jarzynski equality in terms of microscopic reversibility

“…Θ is the antilinear time reversal operator, and P R (Θ|b m → Θ|a n ) is the probability that the time reversed process Π * occurs, namely at t = 0, we perform the measurement aboutB and find the initial state as Θ|b m according to the ensemble with the time reversed density matrix Θρ(T ) ← − Θ and at t = T perform the measurement about and find the final state as Θ|a n . We note that in [13] the average over P F (|α 0 → |α T ) of the logarithm of the ratio…”

“…In order to perform this, we derive the relation (3). In [13] for the case of time independent system, the relation (3) was discussed, however, this relation is necessary for the derivation of fluctuation theorem here, we show the derivation.…”

Time‐Reversal Symmetry Relations for Currents in Quantum and Stochastic Nonequilibrium Systems

“…Similar considerations have been developed for quantum systems [43,113]. We notice that quantum mechanics naturally limits the randomness on the scale where ∆ε∆t = 2π , as explained in Ref.…”

“…In this regard, dynamical order manifests itself away from equilibrium [40]. Furthermore, the breaking of detailed balancing between forward and reversed histories is directly related to the thermodynamic entropy production, as established for classical, stochastic and quantum systems [36][37][38][39][40][41][42][43].…”

“…Moreover, further time-reversal symmetry relations have also been obtained for the probabilities of the histories or paths followed by a system under stroboscopic observations [36][37][38][39][40][41][42][43]. It turns out that the time asymmetry of nonequilibrium statistical distributions implies that typical histories are more probable than their corresponding time reversal.…”