Second law of thermodynamics animation [Mechanical engineering]

# Second law of thermodynamics animation

The Bayesian Second Law of Thermodynamics

Abstract: 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 experimenter's 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 refined versions of the Second Law that bound the entropy increase from below by a non-negative number, as well as Bayesian versions of the Jarzynski equality. We demonstrate the formalism using simple analytical and numerical examples.

### Submission history

From: Anthony Bartolotta [view email]

You might also like
Tutorial on Second law of Thermodynamics

 Entropy - God's Dice Game: The book describes the historical evolution of the understanding of entropy, alongside biographies of the scientists who ... communication theory, economy, and sociology Book (CreateSpace Independent Publishing Platform) Used Book in Good Condition

### FAQ

##### What's the second law of thermodynamics.

It's a general principle which places constraints upon the direction of heat transfer and the attainable efficiencies of ..more?