​Stories about research. 
 

In 1865, Maxwell returned to his family home at Glenlair after leaving his position at King’s College London. A few years later, in 1867, he wrote a letter to Peter Guthrie Tait in which he described Maxwell’s demon, a thought experiment about an intelligent being that seems able to break the second law of thermodynamics.  

The first time you hear about Maxwell’s demon you may find it a strange idea.  It is not easy to see how Maxwell's demon fits within classical mechanics.  However, the more you start thinking about this idea, the more you start seeing links between thermodynamics, information, and computing, and you realise this is a really interesting problem.   I wonder whether Maxwell would have foreseen how much interest his idea would bring?  

Maxwell’s demon is an example of a perpetuum mobile. These are setups that on first sight appear to break the second law of thermodynamics. The second law is a postulate or conjecture about the laws of physics.  Although physicists are strongly convinced about the universal validity of the second law of thermodynamics, the fact that it remains unproven shows it is not fully understood .  This means that one can learn something interesting by looking for counter examples.   

What is so interesting about Maxwell's demon is that the second law is not resovled due to some clever mechanical devie, but because of the knowledge that the demn has about the system.   Apparently, knowledge comes with a thermodynamic sost.   The questions iw how exactly, whether it is in the acquisition of knowledge (measurement), in processing knowledge (cmpoutation), or in its storage (erasure).   It took several decades to resolve this puzzle fully.   Following works of several researchers, including, Brioullin, Szilard and Landauer, it was finally Bennett who put the pieces together.  As he has shown, measurement and computaion do not come with a cost. However, storage of information does, and imporantly, the cost of storage alone is sufficient to resolve Maxwell's puzzle.   The ideas were later generalised  Sagawa e and Ueda generalised using stochastic thermodynamics, a modern version of thermodynamics that combines nonequilibrium thermodynamics with statistical physics.   

So what is new about Maxwell's demon and why did I write a paper on this problem?  Recently, several researchers came up with setups that do not store the state of the sstem, but.  In these soups, the demon always moves the in the same direction, bu the time changes (see figure 2).   Differently than standard septs, the information is temporal.  Intirguilign, such setups also can overcome.  For example, et al, show that a heat engine can overcome Carnot's limit of thermodynamics,.    

In the paper, a resolution for such temporal demons is provided.   The key isnight is that temporal information plays s similar role as spatial one..  One needs to consider a memory device.   Using the stochastic thermodynamics of trajectory dependent variables, we find that this second law is uphold.  Hence, temporal information should be treated on the same footing as spatial information, and this is sufficient to uphold the second law.

Are there other contexts in which time plays an importaont role? One possible view is how demons can measure the time.   time is a somewhat overlooked aspect of Maxwell demons and thermodynamics.  For examle, demons also need a clock to operate, and operating a clock at finite precision comes at a cost, ut this is tno mentioend in classkcal works on Maxwell demons, probably because such systems can use an imprecise clock, and they will be fine.    However, these temporal demosn need a precise clock. .  

Created on October 2025. License: CC BY 4.0