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The Bayesian Second Law of Thermodynamics

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 نشر من قبل Sean Carroll
 تاريخ النشر 2015
  مجال البحث فيزياء
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We derive a generalization of the Second Law of Thermodynamics that uses Bayesian updates to explicitly incorporate the effects of a measurement of a system at some point in its evolution. By allowing an experimenters knowledge to be updated by the measurement process, this formulation resolves a tension between the fact that the entropy of a statistical system can sometimes fluctuate downward and the information-theoretic idea that knowledge of a stochastically-evolving system degrades over time. The Bayesian Second Law can be written as $Delta H(rho_m, rho) + langle mathcal{Q}rangle_{F|m}geq 0$, where $Delta H(rho_m, rho)$ is the change in the cross entropy between the original phase-space probability distribution $rho$ and the measurement-updated distribution $rho_m$, and $langle mathcal{Q}rangle_{F|m}$ is the expectation value of a generalized heat flow out of the system. We also derive refin



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