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The Second Law of Thermodynamics allows for the entropy to remain the same regardless of the direction of time. If the entropy is constant in either direction of time, there would be no preferred direction. However, the entropy can only be a constant if the system is in the highest possible state of disorder, such as a gas that always was, and always will be, uniformly spread out in its container. The existence of a thermodynamic arrow of time implies that the system is highly ordered in one time direction only, which would by definition be the "past". Thus this law is about the boundary conditions rather than the equations of motion.

The Second Law of Thermodynamics allows for the entropy to remain the same regardless of the direction of time. If the entropy is constant in either direction of time, there would be no preferred direction. However, the entropy can only be a constant if the system is in the highest possible state of disorder, such as a gas that always was, and always will be, uniformly spread out in its container. The existence of a thermodynamic arrow of time implies that the system is highly ordered in one time direction only, which would by definition be the "past". Thus this law is about the boundary conditions rather than the equations of motion.

 

 

The Second Law of Thermodynamics is [[statistical]] in nature, and therefore its reliability arises from the huge number of particles present in macroscopic systems. It is not impossible, in principle, for all 6 × 10²³ atoms in a [[Mole (unit)|mole]] of a gas to spontaneously migrate to one half of a container; it is only ''fantastically'' unlikely—so unlikely that no macroscopic violation of the Second Law has ever been observed. [[T Symmetry]] is the symmetry of physical laws under a time reversal transformation. Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.

The Second Law of Thermodynamics is [[statistical]] in nature, and therefore its reliability arises from the huge number of particles present in macroscopic systems. It is not impossible, in principle, for all 6 × 10²³ atoms in a [[Mole (unit)|mole]] of a gas to spontaneously migrate to one half of a container; it is only ''fantastically'' unlikely—so unlikely that no macroscopic violation of the Second Law has ever been observed. [[T Symmetry]] is the symmetry of physical laws under a time reversal transformation. Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.

The Second Law of Thermodynamics is statistical in nature, and therefore its reliability arises from the huge number of particles present in macroscopic systems. It is not impossible, in principle, for all 6 × 10²³ atoms in a mole of a gas to spontaneously migrate to one half of a container; it is only fantastically unlikely—so unlikely that no macroscopic violation of the Second Law has ever been observed. T Symmetry is the symmetry of physical laws under a time reversal transformation. Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.

The Second Law of Thermodynamics is statistical in nature, and therefore its reliability arises from the huge number of particles present in macroscopic systems. It is not impossible, in principle, for all 6 × 10²³ atoms in a mole of a gas to spontaneously migrate to one half of a container; it is only fantastically unlikely—so unlikely that no macroscopic violation of the Second Law has ever been observed. T Symmetry is the symmetry of physical laws under a time reversal transformation. Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.

 

 

The thermodynamic arrow is often linked to the cosmological arrow of time, because it is ultimately about the [[boundary conditions]] of the early universe. According to the [[Big Bang]] theory, the [[Universe]] was initially very hot with energy distributed uniformly. For a system in which [[gravity]] is important, such as the universe, this is a low-entropy state (compared to a high-entropy state of having all matter collapsed into [[black hole]]s, a state to which the system may eventually evolve). As the Universe grows, its temperature drops, which leaves less energy available to perform work in the future than was available in the past. Additionally, [[Perturbation theory (quantum mechanics)|perturbation]]s in the energy density grow (eventually forming [[galaxy|galaxies]] and [[star]]s). Thus the Universe itself has a well-defined thermodynamic arrow of time. But this does not address the question of why the initial state of the universe was that of low entropy. If cosmic expansion were to halt and reverse due to gravity, the temperature of the Universe would once again grow hotter, but its entropy would also continue to increase due to the continued growth  of perturbations and the eventual [[black hole]] formation,<ref>Penrose, R. ''[[The Road to Reality]]'' pp. 686-734</ref> until the latter stages of the [[Big Crunch]] when entropy would be lower than now.{{citation needed|date=June 2012}}

The thermodynamic arrow is often linked to the cosmological arrow of time, because it is ultimately about the [[boundary conditions]] of the early universe. According to the [[Big Bang]] theory, the [[Universe]] was initially very hot with energy distributed uniformly. For a system in which [[gravity]] is important, such as the universe, this is a low-entropy state (compared to a high-entropy state of having all matter collapsed into [[black hole]]s, a state to which the system may eventually evolve). As the Universe grows, its temperature drops, which leaves less energy available to perform work in the future than was available in the past. Additionally, [[Perturbation theory (quantum mechanics)|perturbation]]s in the energy density grow (eventually forming [[galaxy|galaxies]] and [[star]]s). Thus the Universe itself has a well-defined thermodynamic arrow of time. But this does not address the question of why the initial state of the universe was that of low entropy. If cosmic expansion were to halt and reverse due to gravity, the temperature of the Universe would once again grow hotter, but its entropy would also continue to increase due to the continued growth  of perturbations and the eventual [[black hole]] formation,<ref>Penrose, R. ''[[The Road to Reality]]'' pp. 686-734</ref> until the latter stages of the [[Big Crunch]] when entropy would be lower than now.{{citation needed|date=June 2012}}

The thermodynamic arrow is often linked to the cosmological arrow of time, because it is ultimately about the boundary conditions of the early universe. According to the Big Bang theory, the Universe was initially very hot with energy distributed uniformly. For a system in which gravity is important, such as the universe, this is a low-entropy state (compared to a high-entropy state of having all matter collapsed into black holes, a state to which the system may eventually evolve). As the Universe grows, its temperature drops, which leaves less energy available to perform work in the future than was available in the past. Additionally, perturbations in the energy density grow (eventually forming galaxies and stars). Thus the Universe itself has a well-defined thermodynamic arrow of time. But this does not address the question of why the initial state of the universe was that of low entropy. If cosmic expansion were to halt and reverse due to gravity, the temperature of the Universe would once again grow hotter, but its entropy would also continue to increase due to the continued growth  of perturbations and the eventual black hole formation, until the latter stages of the Big Crunch when entropy would be lower than now.

The thermodynamic arrow is often linked to the cosmological arrow of time, because it is ultimately about the boundary conditions of the early universe. According to the Big Bang theory, the Universe was initially very hot with energy distributed uniformly. For a system in which gravity is important, such as the universe, this is a low-entropy state (compared to a high-entropy state of having all matter collapsed into black holes, a state to which the system may eventually evolve). As the Universe grows, its temperature drops, which leaves less energy available to perform work in the future than was available in the past. Additionally, perturbations in the energy density grow (eventually forming galaxies and stars). Thus the Universe itself has a well-defined thermodynamic arrow of time. But this does not address the question of why the initial state of the universe was that of low entropy. If cosmic expansion were to halt and reverse due to gravity, the temperature of the Universe would once again grow hotter, but its entropy would also continue to increase due to the continued growth  of perturbations and the eventual black hole formation, until the latter stages of the Big Crunch when entropy would be lower than now.

热力学箭头通常与宇宙学的时间箭头联系在一起，因为它最终与早期宇宙的边界条件有关。根据大爆炸理论，宇宙最初是非常热的，能量分布均匀。对于一个引力很重要的系统，比如宇宙，这是一个低熵状态(与所有物质坍缩成黑洞的高熵状态相比，系统最终可能进化到这种状态)。随着宇宙的发展，它的温度下降，这使得未来可用于工作的能量比过去要少。此外，能量密度中的扰动也在增加(最终形成星系和恒星)。因此，宇宙本身有一个定义明确的热力学时间箭头。但是这并没有解决为什么宇宙的初始状态是低熵的问题。如果宇宙膨胀由于引力而停止或逆转，那么宇宙的温度将再次升高，但是由于扰动的持续增长和最终黑洞的形成，宇宙的熵也将继续增加，直到大坍缩的后期，那时的熵将比现在低。

热力学箭头经常与时间的宇宙学箭头联系在一起，因为它最终与早期宇宙的边界条件有关。根据大爆炸理论，宇宙最初非常热，能量均匀分布。在重力很重要的系统（比如宇宙）中，这是一种低熵状态(相比之下，所有物质都坍缩成黑洞的高熵状态，系统最终可能会演化到这种状态)。宇宙温度随着发展而下降，未来可用于运转的能量比过去更少。此外，能量密度的扰动会增加(最终形成星系和星体)。因此，宇宙本身就有一个定义明确的热力学时间箭头。但这并没有解决宇宙的初始状态为什么是低熵的问题。如果宇宙膨胀由于重力而停止和逆转，宇宙的温度将再次变得更高，但由于扰动持续增长和最终黑洞形成，宇宙的熵也将继续增加，直到大破裂的后期，那时的熵将比现在更低。

 

 

==An example of apparent irreversibility==

==An example of apparent irreversibility==