# Research Notes, Autumn 2013

These are some ideas stimulated by my research; I write them to make sure I think about / understand certain questions.

Some sections will be quite rough / unintelligible.

# Extending the Second Law of Thermodynamics

\label{sec:t2}

## Alternative Reservoirs

I want to extend the Second Law of Thermodynamics, to include not only heat and information reservoirs, but also reservoirs of other conserved quantities such as angular momentum (see Vaccaro et al. (2011)). What are the implications for the Second Law? Can we derive new statement of the Second Law from a Hamiltonian framework, as in Deffner et al. (2013)?

AG says such ideas are ‘pathological’ – they are not in the spirit of statistical mechanics, which never considers angular momentum.

## Reversible Computation and Maxwell’s Demon

What would be the consequences of reversible computation on the form of the Second Law given in Deffner et al. (2013)? A reversible computation could involve no information erasure and hence no heat dissipation. What would the consequences be for Maxwell’s Demon?

According to Landauer, computer states evolve irreversibly (many-to-one processes). This means the “informative degrees of freedom” (IDF) entropy decreases. BUT, why are the IBF so important? They aren’t physically meaningful, only meaningful to us. The physical quantity would surely be the entropy of all the DoF combined. So, the entropy of IDF is said to increase because the operation is irreversible, but could this be a value judgement?

See here and here for reversible computing info.

I don’t see how you can not lose energy when erasing a bit – even for reversible computation, surely you just dissipate twice as much heat as before (if you go forwards then backwards)? The path is important, not just the end states.

Erasing information is irreversible. Full cycle of MD requires erasing any information that the demon wrote down. Bennet 1982 – quantify information. Thermodynamic entropy different from information theory entropy, as latter invokes no temperature or reservoir.

## Misc

More reading: Mandal et al. (2013)

What is the effect of renormalising on the work of the Demon? On the nature of information?

Does it cost to process information? The answer can be surmised from the realisations of MD.