Why does friction tend to slow the objects? I was biking on the road when suddenly realized a question, that why does friction tend to slow the objects(when the "engine" wasn't doing the "external" work, of course)?
A naive approach was explained in the entropy dynamics. If thinking the bike as an isolated object and the road as the reservoir, then the bike stopped on the ground was actually an equilibrium states, while the bike moving on the road could be considered as strongly interacting. Thus, by maximizing the entropy to achieve the thermalization, a phenomenological force, i.e. friction, must be slowing the bike down. This explanation actually made sense of why the road become slipper when covered by the liquid such as the water or the oil, for it reduced the interaction and thus slowed down the thermalization process.
That's a naive explanation, of course, and it's given by the known results, so it felt less scientific. Is there a way to derive the result from the first principle?
Some attempted thinking:

*

*The Lagrangian might be a bit hard since friction wasn't exactly a potential,

*but could it be described as some sort of the damping in the Hamiltonian?(The hard question was how to make it generic)

*However, both those approach did not take into account for the statistical nature,

*or does it actually require the QFT treatment to describe the in elastic process and the particle motion in the most fundamental way?

*A pictorial illustration suggested that a non linear gradient might be generated from the pressure when the object move forward.

Why does friction tend to slow the objects? and how to prove the phenomenon?
 A: Since your example is about rolling I'll add the following note.

*

*Ideally, the bike is actually not slowed down via friction. Pure rolling does not cause kinetic friction. Thus no work is done against the motion due to (external) friction.


*Realistically, there will be many sources of energy loss that cause conversion of kinetic energy to heat causing a reduction in speed. But they won't be (external) friction.
Compression/expansion of rubber causing internal work and thus heat loss, frictions within axles and gears, work done on soft surfaces (like a sandy beach), and the like all cause energy loss that slow down the motion. Also, non-ideal, non-point-like contact between wheel and road will cause normal forces that are not directed towards the wheel centre and that thus might cause counteracting torques that also slow down the motion. These factors are very real but are not road-to-wheel friction.
All such factors are often under one name called rolling friction, which is slightly misleading since we are not dealing with external friction. If you want to look into the thermodynamic details of where to and how the energy dissipates then you should look into each of these different possible causes of energy loss individually and for each of them apply an appropriate analysis. I wouldn't recommend looking purely at friction since that is not the main cause - if any - of you slowing down while driving.
When dealing with friction during sliding rather than rolling, then it's a different scenario and your questions are applicable.
A: The direction of frictional force is opposite to the relative velocities of the objects.   So, friction does not slow objects
in general, but only if an object causing friction is considered to be stationary.
An object on my car's dashboard slips a bit, but comes
to "rest" at the same forward velocity as the car, rather than zero
miles per hour like the pavement below.
The planetary surface that road is attached to,
still spins at a similar rate to a century ago, for instance. Friction against the planet hasn't stopped it.
