The question might have some misconceptions/ sloppy intuition sorry if that's the case (I m not a physicist).

I seem to have the intuition that given a system of $N$ charged particles in $3$D space colliding (under the effect of gravitational forces and electrostatic forces) elastically with each other, then the evolution of this system is symmetric with respect to time reversal. In the sense that if I record a video of the evolution of this mechanical system and then play it backwards then the resulting video will look like something that can happen in our universe. If this intuition is correct, then it should be easy to prove mathematically from the uniqueness theorem of ordinary differential equations.

I also seem to have the idea that statistical mechanics is nothing but the situation described above with $N$ being very large (particles in a gas are moving under the effect of gravitational and van der waal forces and nothing else, no?). Thus, I would expect that the evolution of a thermodynamic system with respect to time should be symmetric with respect to time reversal. However this seems to contradict the second law of thermodynamics. Where did I go wrong?

After seeing some of the responses to my question I wish to add the following :

I am NOT trying to refute the second law mathematically (lol :D). As you can see above I don't provide any mathematical proofs . I specifically said "If my intuition is correct, then it should be easy to prove mathematically ". That means I am skeptical about my own intuition because: 1) I don't back it up with a proof  , 2)it is in contradiction with a well established law such as the second law.

The question might have some misconceptions/ sloppy intuition sorry if that's the case (I'm not a physicist).

I seem to have the intuition that given a system of $N$ charged particles in 3D space colliding (under the effect of gravitational forces and electrostatic forces) elastically with each other, then the evolution of this system is symmetric with respect to time reversal. In the sense that if I record a video of the evolution of this mechanical system and then play it backwards then the resulting video will look like something that can happen in our universe. If this intuition is correct, then it should be easy to prove mathematically from the uniqueness theorem of ordinary differential equations.

I also seem to have the idea that statistical mechanics is nothing but the situation described above with $N$ being very large (particles in a gas are moving under the effect of gravitational and van der Waal forces and nothing else, no?). Thus, I would expect that the evolution of a thermodynamic system with respect to time should be symmetric with respect to time reversal. However this seems to contradict the second law of thermodynamics. Where did I go wrong?

After seeing some of the responses to my question I wish to add the following :

I am NOT trying to refute the second law mathematically (lol :D). As you can see above I don't provide any mathematical proofs . I specifically said "If my intuition is correct, then it should be easy to prove mathematically ". That means I am skeptical about my own intuition because: 1) I don't back it up with a proof, 2) it is in contradiction with a well established law such as the second law.

The question might have some misconceptions/ sloppy intuition sorry if that's the case (I m not a physicist).

I seem to have the intuition that given a system of $N$ charged particles in $3$D space colliding (under the effect of gravitational forces and electrostatic forces) elastically with each other, then the evolution of this system is symmetric with respect to time reversal. In the sense that if I record a video of the evolution of this mechanical system and then play it backwards then the resulting video will look like something that can happen in our universe. If this intuition is correct, then it should be easy to prove mathematically from the uniqueness theorem of ordinary differential equations.

I also seem to have the idea that statistical mechanics is nothing but the situation described above with $N$ being very large (particles in a gas are moving under the effect of gravitational and van der waal forces and nothing else, no?). Thus, I would expect that the evolution of a thermodynamic system with respect to time should be symmetric with respect to time reversal. However this seems to contradict the second law of thermodynamics. Where did I go wrong?

The question might have some misconceptions/ sloppy intuition sorry if that's the case (I m not a physicist).

I seem to have the intuition that given a system of $N$ charged particles in $3$D space colliding (under the effect of gravitational forces and electrostatic forces) elastically with each other, then the evolution of this system is symmetric with respect to time reversal. In the sense that if I record a video of the evolution of this mechanical system and then play it backwards then the resulting video will look like something that can happen in our universe. If this intuition is correct, then it should be easy to prove mathematically from the uniqueness theorem of ordinary differential equations.

I also seem to have the idea that statistical mechanics is nothing but the situation described above with $N$ being very large (particles in a gas are moving under the effect of gravitational and van der waal forces and nothing else, no?). Thus, I would expect that the evolution of a thermodynamic system with respect to time should be symmetric with respect to time reversal. However this seems to contradict the second law of thermodynamics. Where did I go wrong?

After seeing some of the responses to my question I wish to add the following :

I am NOT trying to refute the second law mathematically (lol :D). As you can see above I don't provide any mathematical proofs . I specifically said "If my intuition is correct, then it should be easy to prove mathematically ". That means I am skeptical about my own intuition because: 1) I don't back it up with a proof , 2)it is in contradiction with a well established law such as the second law.

The question might have some misconceptions/ sloppy intuition sorry if that's the case (I m not a physicist).

I seem to have the intuition that given a system of $N$ charged particles in $3$D space colliding (under the effect of gravitational forces and electrostatic forces) elastically with each other, then the evolution of this system is symmetric with respect to time reversal. In the sense that if I record a video of the evolution of this mechanical system and then play it backwards then the resulting video will look like something that can happen in our universe. If this intuition is correct, then it should be easy to prove mathematically from the uniqueness theorem of ordinary differential equations.

I also seem to have the idea that statistical mechanics is nothing but the situation described above with $N$ being very large (particles in a gas are moving under the effect of gravitational and van der waal forces and nothing else, no?). Thus, I would expect that the evolution of a thermodynamic system with respect to time should be symmetric with respect to time reversal. However this seems to contradict the second law of thermodynamics. Where did I go wrong  ?

The question might have some misconceptions/ sloppy intuition sorry if that's the case (I m not a physicist).

I seem to have the intuition that given a system of $N$ charged particles in $3$D space colliding (under the effect of gravitational forces and electrostatic forces) elastically with each other, then the evolution of this system is symmetric with respect to time reversal. In the sense that if I record a video of the evolution of this mechanical system and then play it backwards then the resulting video will look like something that can happen in our universe. If this intuition is correct, then it should be easy to prove mathematically from the uniqueness theorem of ordinary differential equations.

I also seem to have the idea that statistical mechanics is nothing but the situation described above with $N$ being very large (particles in a gas are moving under the effect of gravitational and van der waal forces and nothing else, no?). Thus, I would expect that the evolution of a thermodynamic system with respect to time should be symmetric with respect to time reversal. However this seems to contradict the second law of thermodynamics. Where did I go wrong?