The hudson parthasarathy quantum stochastic differential equation can be solved by a classical integral in a high dimensional space with the help of an a priori estimate it is possible to show . Stochastic quantum mechanics or the stochastic interpretation is an interpretation of quantum mechanics the modern application of stochastics to quantum mechanics involves the assumption of spacetime stochasticity the idea that the small scale structure of spacetime is undergoing both metric and topological fluctuations john archibald wheelers quantum foam and that the averaged . In quantum mechanics each physical system is associated with a hilbert spacethe approach codified by john von neumann represents a measurement upon a physical system by a self adjoint operator on that hilbert space termed an observable 17 these observables play the role of measurable quantities familiar from classical physics position momentum energy angular momentum and so on. This article sets up a new formalism to investigate stochastic thermodynamics in the quantum regime where stochasticity and irreversibility primarily come from quantum measurement in the absence . In order to describe rigorously certain measurement procedures where observations of the arrival of quanta at a counter are made throughout an interval of time it is necessary to introduce the concept of a quantum stochastic process while fully quantum mechanical in nature these have a great deal of similarity with classical stochastic
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