The Landauer limit L(T) = kTln2, k is the Boltzmann constant, means the energy corresponding to erasing a single bit of information. Thus, one can define t(T)=kTln2/h, h - the Planck constant. What might be the physical meaning of the so-defined function t(T) or that of its reverse function T(t)? Furthermore, t can be referred as f=1/t to the frequency of some wave having a certain physical sense.
A few general considerations might be:
1. The Planck constant means the correspondence of a dimensionless physical quantity to the quantity of action. That dimensionless physical quantity can be interpreted as entropy.
2. The Landauer limit means energy per a bit of information (entropy).
3, Action is a function of energy and time and thus, time as temperature can be interpreted as a relation (e.g. ratio) of energy and entropy.
4. Then, the dependence of time and temperature at both Landauer limit and Planck constant for both time and temperature are interpreted only by energy and entropy as above implies both time and temperature to be referred to the same state of affairs from two different viewpoints: (quantum) mechanics for time, and thermodynamics for temperature.
5. That idea (4) implies that energy and entropy in turn can be seen as the same quantity from two different viewpoints, and time and temperature represent the difference between the latter two viewpoints from the former two viewpoints accordingly of (quantum) mechanics and thermodynamics.
6. That quantity described whether as time or as temperature means intuitively the transition "inside - outside", or a little more exact: the transition "inside of a physical system" to "outside of the same system". That transition in (quantum) mechanics is called motion and mathematically described as a function of time. It means that system as a single whole conventionally called "particle", which is moving from the past position ("inside") to the future position ("outside") right now. That transition seems not to be called in thermodynamics (at least, I cannot guess how),but it means the transition from considering the system as consisting of many, many elements (“inside”) to a thermodynamic whole (“outside”).
Defined slightly differently this is related to the Matsubara frequency which is wide used in the statistical physics.
Yes, the Matsubara frequency turns out to be the same. However, it has not any physical sense as well: only a mathenatical tool with the physical dimensionality of frequency associable with temperature in solid-state physics. If one interprets it as the frequency of some wave, this would address a certain physical interpretation.
@Vasil Dinev Penchev,
I like you to double check your formula, t(T)=kTln2/h. I suspect some problem. Energy E = L(T) should be defined as E = hf = h/t where f is the frequency and t the period of the wave. From this your formula should be written as f = 1/t = kTln2/h. In this formula there are only two variables, rest are all constants. These two variables are inversely proportional to each other. t (period) is inversely proportional to T(temperature). Or frequency is directly proportional to temperature.
Yes, I mean right the same, maybe it is not clear enough. So. thank you for the elucidation. Anyway that formula might be only a particular case of some more general function T(t), T(f). t(T). or f(T). This is the reason for my formulation.
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