Starting from Landauer's slogan "information is physical," we revise and modify Landauer's principle stating that the erasure of information has a minimal price in the form of a certain quantity of free energy. We establish a direct link between the erasure cost and the work value of a piece of information and show that the former is essentially the length of the string's best compression by a reversible computation. We generalize the principle by deriving bounds on the free energy to be invested for-or gained from, for that matter-a general computation. We then revisit the second law of thermodynamics and compactly rephrase it (assuming the Church-Turing-Deutsch hypothesis that physical reality can be simulated by a universal Turing machine): Time evolutions are logically reversible-"the future fully remembers the past (but not necessarily vice versa)." We link this view to previous formulations of the second law, and we argue that it has a particular feature that suggests its "logico-informational" nature, namely, simulation resilience: If a computation faithfully simulates a physical process violating the law, then that very computation procedure violates it as well.