Abstract
We consider a typical master equation describing thermal time-evolution. In parallel, we also consider a quasi static canonical description of the same problem. We are able to devise a way of numerically comparing these two treatments and concoct a distance-measure between them. In this way, one is in a position to know how far or close equilibrium and off-equilibrium can get. The first, rather surprising observation, is that our systems lose structural details as N grows. Also, the time-evolution of the distance between the two pertinent probability distributions is quite sensitive to the heating-cooling process.
Highlights
The time-evolution of the distance between the two pertinent probability distributions is quite sensitive to the heating-cooling process
Our aim is to derive the time evolution of the probability distribution (PD) for the entire system A + B, in a way which guarantees that normalization is preserved at any time t
The solution to this problem is found in the so-called master equation (ME) technique [1]
Summary
Researchers often appeal to master equations (ME) to obtain an equation of motion for the reduced density operator. Our aim is to derive the time evolution of the PD for the entire system A + B, in a way which guarantees that normalization (amongst other properties) is preserved at any time t. The solution to this problem is found in the so-called master equation (ME) technique [1]. A popular, but not rigorous ME-approach can be used in the case of physical situations for which interacting systems A and B are known and well-defined so that one constructs the corresponding ME-equation of motion for the PD [1]. A beautiful instantiation of the ME-procedure is presented by Takada, Conradt, and Richet (TCR) in [2], for example, we will follow here without further ado
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