We make this link precise by showing under which conditions a negative entropy production rate implies non-Markovianity and when it does not. For a system coupled to a single heat bath, this can be established within a unified language for two setups: i the dynamics resulting from a coarse-grained description of a Markovian master equation and ii the classical Hamiltonian dynamics of a system coupled to a bath.
The quantum version of the latter result is shown not to hold despite the fact that the integrated thermodynamic description is formally equivalent to the classical case. The instantaneous fixed point of a non-Markovian dynamics plays an important role in our study. Our key contribution is to provide a consistent theoretical framework to study the finite-time thermodynamics of a large class of dynamics with a precise link to its non-Markovianity.
A Venn diagram to understand the implications of Theorem t6.
The largest outer box contains all possible lumped stochastic process. One subset of them is 1-Markovian shaded in gray. In the long-time limit, the IFP coincides with the equilibrium distribution The system was prepared according to Eq.
Note that this specific choice corresponds to equilibrated covariances, but the mean values are out of equilibrium. The general features of the plot, however, do not change too much for different nonequilibrium initial states. See also Ref. Overview of the results from Secs.
The arrows indicate implications in a mathematical sense. Some implications depend on certain conditions, which are marked by a line attached with a circle to the respective arrow. E 99 , — Published 14 January Abstract Entropy production plays a fundamental role in nonequilibrium thermodynamics to quantify the irreversibility of open systems. Research Areas. Brownian motion Entropy production Irreversible processes Nonequilibrium statistical mechanics Open quantum systems Quantum thermodynamics.stosvitthinknorth.tk
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