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Register a new userFluctuation theorems from Bayesian retrodiction
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Quantitative studies of irreversibility in statistical mechanics often involve the consideration of a reverse process, whose definition has been the object of many discussions, in particular for quantum mechanical systems. Here we show that the reverse channel very naturally arises from Bayesian retrodiction, both in classical and quantum theories. Previous paradigmatic results, such as Jarzynskis equality, Crooks fluctuation theorem, and Tasakis two-measurement fluctuation theorem for closed driven quantum systems, are all shown to be consistent with retrodictive arguments. Also, various corrections that were introduced to deal with nonequilibrium steady states or open quantum systems are justified on general grounds as remnants of Bayesian retrodiction. More generally, with the reverse process constructed on consistent logical inference, fluctuation relations acquire a much broader form and scope.
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Irreversibility is usually captured by a comparison between the process that happens and a corresponding reverse process. In the last decades, this comparison has been extensively studied through fluctuation relations. Here we revisit fluctuation relations from the standpoint, suggested decades ago by Watanabe, that the comparison should involve the prediction and the retrodiction on the unique process, rather than two processes. We identify a necessary and sufficient condition for a retrodictive reading of a fluctuation relation. The retrodictive narrative also brings to the fore the possibility of deriving fluctuation relations based on various statistical divergences, and clarifies some of the traditional assumptions as arising from the choice of a reference prior.
This work brings together Keldysh non-equilibrium quantum theory and thermodynamics, by showing that a real-time diagrammatic technique is an equivalent of stochastic thermodynamics for non-Markovian quantum machines (heat engines, refrigerators, etc). Symmetries are found between quantum trajectories and their time-reverses on the Keldysh contour, for any interacting quantum system coupled to ideal reservoirs of electrons, phonons or photons. These lead to quantum fluctuation theorems the same as the well-known classical ones (Jarzynski and Crooks equalities, integral fluctuation theorem, etc), whether the systems dynamics are Markovian or not. Some of these are also shown to hold for non-factorizable initial states. The sequential tunnelling approximation and the cotunnelling approximation are both shown to respect the symmetries that ensure the fluctuation theorems. For all initial states, energy conservation ensures that the first law of thermodynamics holds on average, while the above symmetries ensures that the second law of thermodynamics holds on average, even if fluctuations violate it. [ERRATUM added: March 2021]
Active biological systems reside far from equilibrium, dissipating heat even in their steady state, thus requiring an extension of conventional equilibrium thermodynamics and statistical mechanics. In this Letter, we have extended the emerging framework of stochastic thermodynamics to active matter. In particular, for the active Ornstein-Uhlenbeck model, we have provided consistent definitions of thermodynamic quantities such as work, energy, heat, entropy, and entropy production at the level of single, stochastic trajectories and derived related fluctuation relations. We have developed a generalization of the Clausius inequality, which is valid even in the presence of the non-Hamiltonian dynamics underlying active matter systems. We have illustrated our results with explicit numerical studies.
In this work, a physical system described by Hamiltonian $mathbf{H}_omega = mathbf{H}_0 + mathbf{V}_omega(mathbf{x},t)$ consisted of a solvable model $mathbf{H}$ and external random and time-dependent potential $mathbf{V}_omega(mathbf{x},t)$ is investigated. Under the conditions that the average external potential with respect to the configuration $omega$ is constant in time, and, for each configuration, the potential changes smoothly that the evolution of the system follows Schrodinger dynamics, the mean-dynamics can be derived from taking average of the equation with respect to configuration parameter $omega$. It provides extra contributions from the deviations of the Hamiltonian and evolved state along the time to the Heisenberg and Liouville-von Neumann equations. Consequently, the Kubos formula and the fluctuation-dissipation relation obtained from the construction is modified in the sense that the contribution from the information of randomness and memory effect from time-dependence are present.
This is a reply to the comment to a letter by D. Mandal, K. Klymko and M. R. DeWeese published as Phys. Rev. Lett. 119, 258001 (2017).
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