“All known microscopic dynamical laws (such as those that underpin classical and quantum mechanics) are time-reversible (meaning that taking a physical evolution and ‘reversing’ the direction of time leads to an equally valid physical evolution). However, the second law of thermodynamics is time-irreversible. Since the macroscopic systems which obey the second law are composed of microscopic components, all of which must obey the reversible dynamical laws, we have reached a paradox, since it should not be possible to derive an irreversible process from time-symmetric dynamics. This is known as Loschmidt’s Paradox. ”
“Some proposals claim to have solved this paradox by coarse-graining or averaging over physical states. For example, one can describe the second law in terms of the increase in entropy and entropy as a measure of uncertainty of an observer (see eg. this piece). These solutions are very elegant, but also make thermodynamics into a claim about knowledge. ”
The paradox arises if one takes the microphysical laws to apply exceptionlessly at all scales. Macrophysical laws are not complete descriptions of reality, because they are coarse grained, treating microphysical behaviour as a statistical average. Microphysical laws are not necessarily complete descriptions of reality, because they might neglect large scale features such as spatial curvature.
If microphysical laws are limited and approximate , there is no reasonable expectation that they could imply macrophysical laws.
Indeed, one could take the opposite view...that microphysical laws are special cases of macrophysical ones. For instance, reversible microphysical laws are only special cases of irreversible macrophysical laws ; determinism is a special case of indeterminism; linearity is a special case of nonlinearity.
“All known microscopic dynamical laws (such as those that underpin classical and quantum mechanics) are time-reversible (meaning that taking a physical evolution and ‘reversing’ the direction of time leads to an equally valid physical evolution). However, the second law of thermodynamics is time-irreversible. Since the macroscopic systems which obey the second law are composed of microscopic components, all of which must obey the reversible dynamical laws, we have reached a paradox, since it should not be possible to derive an irreversible process from time-symmetric dynamics. This is known as Loschmidt’s Paradox. ”
“Some proposals claim to have solved this paradox by coarse-graining or averaging over physical states. For example, one can describe the second law in terms of the increase in entropy and entropy as a measure of uncertainty of an observer (see eg. this piece). These solutions are very elegant, but also make thermodynamics into a claim about knowledge. ”
The paradox arises if one takes the microphysical laws to apply exceptionlessly at all scales. Macrophysical laws are not complete descriptions of reality, because they are coarse grained, treating microphysical behaviour as a statistical average. Microphysical laws are not necessarily complete descriptions of reality, because they might neglect large scale features such as spatial curvature.
If microphysical laws are limited and approximate , there is no reasonable expectation that they could imply macrophysical laws.
Indeed, one could take the opposite view...that microphysical laws are special cases of macrophysical ones. For instance, reversible microphysical laws are only special cases of irreversible macrophysical laws ; determinism is a special case of indeterminism; linearity is a special case of nonlinearity.