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"Thermodynamics is a phenomenological theory" I am not able to understand the difference between empirical and phenomenological descriptions, aren't all theories empirical?? Do we say some description is empirical when we have nothing but some numerical model at hand and we say it is phenomenological we hold some fact to be self-evident even for other situations apart from the ones covered in experiments?

can some explain with examples?? Is friction force, $$F = \mu mg$$ empirical or phenomenological?? or saying that $$F = F(m, g)$$ based on some clever arguments is phenomenological while the fact that this function is a hyperbola is empirical as found from experiments?

Plz explain

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The root of phenomenology comes from "phenomenon" meaning "observed" in ancient greek, but in physics theories it is used to label theories that are used to fit and predict data.

In physics, phenomenology is the application of theoretical physics to experimental data by making quantitative predictions based upon known theories.

Physics theories are really rigorous mathematical constructs, with extra axioms to pick the relevant to physics solutions, and can predict certain data for testing, but usually it is too laborious to do so . Phenomenology developed as applied theory, using tools for approximations in order to give testable by experiment predictions, from the theories, without going into solving rigorously the theories.

Empirical, comes from "empeiria", accumulated experience.

"Thermodynamics is a phenomenological theory"

The theory of thermodynamics developed from accumulated experience and in the beginning was empirical. It now is a rigorous mathematical theory that fits the data so I would not call it a phenomenological theory, and in addition it can be shown to emerge from statistical mechanics.

Axioms/laws of physics theories are empirical, found experimentally. F=ma is a law in Newtonian mechanics and is empirical. In general direct connection to experiment is empirical, the μ for friction for example.

Parabolas are direct and simple solutions of the theory and the term "phenomenology" is inappropriate to describe them. For a complicated solution to a planetary orbit a phenomenological model might be used, to avoid the excessive number of parameters coming into the rigorous solution.

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I don't think that the alternative is between phenomenology and empiricism. Rather, it should probably be between phenomenological theories and "ontological"/fundamental theories.

Basically, a phenomenological theory is one which only pretends to describe some observable phenomena or experiment, without claiming to describe fundamental objects. On the other hand, an "ontological" (or fundamental) theory tries to describe the fundamental constituents and laws of the universe. Slightly more generally, if a theory tries to develop general laws which can be applied in many different situations, we shouldn't call it phenomenological.

For example, Newtonian mechanics (eg the laws of motion and gravity) was trying to establish fundamental laws of natures. We now know that it is not fundamental but only limiting case of quantum/relativistic theories. Nevertheless, it probably shouldn't be called phenomenological, as they apply quite generally to classical mechanics. On the other hand, the expression for some solid friction force is phenomenological.

In all cases, theories in physics should be empirical : developed from and tested against experiments.

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