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Master equation
About: Master equation is a research topic. Over the lifetime, 10541 publications have been published within this topic receiving 276095 citations.
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TL;DR: In this article, it is argued that due to the large number and the randomly varying complex phase angles, these terms tend to cancel each other, so that only the squared terms survive.
134 citations
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TL;DR: A stochastic approach to nonequilibrium thermodynamics based on the expression of the entropy production rate advanced by Schnakenberg for systems described by a master equation is presented, finding a singularity at the critical point of the linear-logarithm type.
Abstract: We present a stochastic approach to nonequilibrium thermodynamics based on the expression of the entropy production rate advanced by Schnakenberg for systems described by a master equation. From the microscopic Schnakenberg expression we get the macroscopic bilinear form for the entropy production rate in terms of fluxes and forces. This is performed by placing the system in contact with two reservoirs with distinct sets of thermodynamic fields and by assuming an appropriate form for the transition rate. The approach is applied to an interacting lattice gas model in contact with two heat and particle reservoirs. On a square lattice, a continuous symmetry breaking phase transition takes place such that at the nonequilibrium ordered phase a heat flow sets in even when the temperatures of the reservoirs are the same. The entropy production rate is found to have a singularity at the critical point of the linear-logarithm type.
134 citations
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TL;DR: An open source computational framework geared towards the efficient numerical investigation of open quantum systems written in the Julia programming language, based on standard quantum optics notation, that offers speed comparable to low-level statically typed languages, without compromising on the accessibility and code readability found in dynamic languages.
134 citations
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TL;DR: Three integral fluctuation theorems are derived for these contributions and it is shown that they lead to the following universal inequality: An arbitrary nonequilibrium transformation always produces a change in the total entropy production greater than or equal to the one produced if the transformation is done very slowly (adiabatically).
Abstract: The total entropy production generated by the dynamics of an externally driven systems exchanging energy and matter with multiple reservoirs and described by a master equation is expressed as the sum of three contributions, each corresponding to a distinct mechanism for bringing the system out of equilibrium: Nonequilibrium initial conditions, external driving, and breaking of detailed balance. We derive three integral fluctuation theorems (FTs) for these contributions and show that they lead to the following universal inequality: An arbitrary nonequilibrium transformation always produces a change in the total entropy production greater than or equal to the one produced if the transformation is done very slowly (adiabatically). Previously derived fluctuation theorems can be recovered as special cases. We show how these FTs can be experimentally tested by performing the counting statistics of the electrons crossing a single level quantum dot coupled to two reservoirs with externally varying chemical potentials. The entropy probability distributions are simulated for driving protocols ranging from the adiabatic to the sudden switching limit.
133 citations
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TL;DR: In this paper, it was shown that the solutions of the master equation and the random walk approach each other at long times and are approximately equal for times much larger than the maximum of (τn/n!)1/n if the eigenvalues and eigenfunctions of A and (M − 1)/τ1 are approxima.
Abstract: It is shown that there is a simple relation between master equation and random walk solutions. We assume that the random walker takes steps at random times, with the time between steps governed by a probability density ψ(Δt). Then, if the random walk transition probability matrix M and the master equation transition rate matrix A are related by A = (M − 1)/τ1, where τ1 is the first moment of Ψ(t) and thus the average time between steps, the solutions of the random walk and the master equation approach each other at long times and are essentially equal for times much larger than the maximum of (τn/n!)1/n, where τn is the nth moment of ψ(t). For a Poisson probability density ψ(t), the solutions are shown to be identical at all times. For the case where A ≠ (M − 1)/τ1, the solutions of the master equation and the random walk approach each other at long times and are approximately equal for times much larger than the maximum of (τn/n!)1/n if the eigenvalues and eigenfunctions of A and (M − 1)/τ1 are approxima...
133 citations