Measurement without energy cost?

[voila]

Hi,

On the context of Maxwell's Demon, it's accepted that Landauer's principle (the erasure of a bit of information requires kTln2 of work) gives a solution to the paradox. The erasure of a bit of information can be seen as the modulation of a double well potential, as in the right side of the red line in the picture.

It's also accepted that measurement can be done without energy expenditure. This was stated by Bennett, who proposed a measuring system just like the one on the left of the red line. Don't worry about the system itself: the important part is that the process can be represented by a double well potential being modulated just like it's drawn next to it.

Well, as far as I can see, both double well potentials undergo the same procedure, yet the left one describes a process with supposedly no energy expenditure and the right one a process with kTln2 of energy expenditure. What am I missing?

 

[AndyW]

Hello,

Thank you for bringing up this interesting topic of Maxwell's Demon and Landauer's principle. You are correct in stating that Landauer's principle provides a solution to the paradox of Maxwell's Demon, which suggests that it is possible to violate the second law of thermodynamics by using a demon to selectively sort particles based on their energy.

In regards to the double well potential, it is important to note that the process of erasing a bit of information is not the same as measuring it. The process of erasure involves reducing the uncertainty of a system by removing a bit of information, while measurement involves obtaining information about the system without changing its state. Therefore, while both processes may involve the modulation of a double well potential, they are fundamentally different and thus have different energy requirements.

Additionally, it is important to consider the role of information in these processes. Landauer's principle states that the erasure of a bit of information requires energy expenditure, but this energy is not being used to change the physical state of the system. Instead, it is being used to reset the system to a known state, which is necessary in order to maintain the second law of thermodynamics. On the other hand, in the process of measurement, the energy required is used to obtain information about the system without changing its state.

In summary, while the processes of erasure and measurement may appear similar in terms of their use of double well potentials, they are fundamentally different and thus have different energy requirements. I hope this helps to clarify any confusion you may have had on the topic. Thank you for your interest in this subject.