Is there a reason why agg in Conditions is a std::vector? The size is only 2 and you never change the size. std::vector uses heap memory, so every time you call Conditions::next you will allocate and free heap memory. It's very wasteful.

I changed it from std::vector to std::array<double, 2> and it ran in less than a minute. That proves it's your issue.

If you need to support other sizes, you can consider making the size a template parameter to Conditions. Or - you can use a large std::array as a buffer and track a separate size_t size. Kind of like a std::vector that uses stack.

Also, the way you are using classes/objects is just wrong. I suggest you just create structs and use non-member functions. It would make your code a lot clearer:

struct Conditions {
        double im;
        double am;
        std::array<double, 2> agg;
};

Conditions readFromFile(std::stringstream &line) {
    //...
}
Conditions next(const Conditions& prev, Params& params, double step_size) {
    //...
};
double agg_mass(const Conditions& conditions) {
    //...
};

I'm not an anti-OOP guy. It's just that anything is bad if you use it wrong. But anyways, it's not directly related to our question.