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Energy dissipation occurs irreversibly through friction and resistance forces, converting ordered mechanical energy into disordered thermal energy. This process breaks time-reversal symmetry and is modeled by dissipation coefficients like damping constants.
From your study of non-conservative forces, you know the essential contrast: a conservative force like gravity stores energy that can be fully recovered — lift a book, lower it, and all the energy is returned as kinetic energy. A non-conservative force like friction does not store energy; it destroys its mechanical form. Energy dissipation names this conversion process precisely: ordered kinetic and potential energy is converted into disordered thermal energy — random molecular motion — and that conversion is one-way.
Why one-way? This is the deep question. The laws of classical mechanics are time-reversible: every solution to Newton's equations has a mirror solution where all velocities are reversed and the system runs backward. A ball bouncing elastically looks the same played in reverse. But a ball rolling to a stop due to friction does not: play it backward, and you see heat spontaneously organizing into ordered motion, which never happens. The irreversibility is not in the equations of motion for individual particles — it emerges from the statistical impossibility of all the disordered thermal motions in the surface and ball spontaneously re-coordinating to push the ball forward. There are astronomically more ways for energy to be spread randomly across molecular degrees of freedom than there are ways for it to be concentrated in a single macroscopic direction of motion. Irreversibility is a statistical near-certainty, not a logical necessity.
In mechanical models, dissipation is captured through damping terms. A frictional force proportional to velocity — the simplest dissipation model — produces exponential decay of amplitude in an oscillator. The damping constant b (or equivalently the damping coefficient γ) quantifies how rapidly energy leaves the mechanical degrees of freedom per unit time. For a mass-spring system with velocity-dependent drag, the equation of motion becomes mẍ + bẋ + kx = 0, and the solution shows amplitude decaying as e−bt/2m. The energy stored in the oscillation decreases at the same exponential rate, flowing irreversibly into the thermal environment.
The concept of irreversibility connects classical mechanics to thermodynamics in a way that turns out to be fundamental. The second law of thermodynamics — that the entropy of an isolated system never decreases — is the macroscopic statement of what dissipation means at the level of bulk material properties. Every time friction converts organized mechanical energy to heat, entropy increases in the universe. This is not a separate empirical law bolted onto mechanics; it is what happens when mechanics is applied to systems with enormous numbers of degrees of freedom. Understanding energy dissipation in classical mechanics is therefore your entry point into one of physics' deepest results: that while the micro-laws of physics are time-symmetric, the macro-world we inhabit has a definite direction of time — and that direction is defined by the one-way flow of energy from order to disorder.