The Second Law Of Thermodynamics: Unbreakable?

The second law of thermodynamics is a physical law based on universal empirical observation concerning heat and energy interconversions. It establishes the concept of entropy as a physical property of a thermodynamic system. The law states that the entropy, or disorder, of the universe increases over time. While the second law of thermodynamics is considered a fundamental principle, with sources citing it as the supreme position among the laws of nature, there have been questions and debates about whether it can be violated.

The second law of thermodynamics is statistical

The second law of thermodynamics is a physical law based on universal empirical observation concerning heat and energy interconversions. It is a definition of the direction of natural processes. It asserts that a natural process runs only in one direction and is not reversible. This is often referred to in the concept of the "arrow of time". For example, it is easy to break a window but hard to fix it.

The second law of thermodynamics can be stated in three synonymous ways:

• For a spontaneous process, the entropy of the universe increases.
• For a spontaneous process, ΔSuniverse > 0.
• For a spontaneous process, ΔSsystem + ΔSsurroundings > 0.

Statistical mechanics postulates that, in equilibrium, each microstate that the system might be in is equally likely to occur. When this assumption is made, it leads directly to the conclusion that the second law must hold in a statistical sense. That is, the second law will hold on average, with a statistical variation on the order of 1/√N where N is the number of particles in the system. For everyday (macroscopic) situations, the probability that the second law will be violated is practically zero. However, for systems with a small number of particles, thermodynamic parameters, including the entropy, may show significant statistical deviations from that predicted by the second law.

Entropy and the second law

The second law of thermodynamics is a physical law based on universal empirical observation concerning heat and energy interconversions. It establishes the concept of entropy as a physical property of a thermodynamic system. The second law of thermodynamics is statistical in nature, and its reliability arises from the huge number of particles present in macroscopic systems.

The second law may be formulated by the observation that the entropy of isolated systems left to spontaneous evolution cannot decrease, as they always tend toward a state of thermodynamic equilibrium where the entropy is highest at the given internal energy. An increase in the combined entropy of a system and its surroundings accounts for the irreversibility of natural processes, often referred to in the concept of the arrow of time. The second law is concerned with the direction of natural processes. It asserts that a natural process runs only in one sense and is not reversible. That is, the state of a natural system itself can be reversed, but not without increasing the entropy of the system's surroundings.

The second law is often false for short time scales. For small systems, the fluctuations of entropy are significant and are often towards decreasing entropy. The second law is violated constantly, everywhere, and at all times at the quantum level. However, for everyday (macroscopic) situations, the probability that the second law will be violated is practically zero.

In 1878, the physicist James Clerk Maxwell wrote in a book review for Nature:

> The truth of the second law is ... a statistical, not a mathematical, truth, for it depends on the fact that the bodies we deal with consist of millions of molecules... Hence the second law of thermodynamics is continually being violated, and that to a considerable extent, in any sufficiently small group of molecules belonging to a real body.

In 2002, researchers showed for the first time that, at the level of thousands of atoms and molecules, fleeting energy increases violate the second law of thermodynamics. They found that over periods of less than two seconds, variations in the random thermal motion of water molecules occasionally gave individual beads a kick. This increased the beads' kinetic energy by a small but significant amount, in apparent violation of the second law.

The second law and the concept of time

The second law of thermodynamics is a physical law based on universal empirical observation concerning heat and energy interconversions. A simple statement of the law is that heat always flows spontaneously from hotter to colder regions of matter. The second law of thermodynamics establishes the concept of entropy as a physical property of a thermodynamic system. It predicts whether processes are forbidden despite obeying the requirement of conservation of energy as expressed in the first law of thermodynamics and provides necessary criteria for spontaneous processes.

The second law may be formulated by the observation that the entropy of isolated systems left to spontaneous evolution cannot decrease, as they always tend toward a state of thermodynamic equilibrium where the entropy is highest at the given internal energy. An increase in the combined entropy of a system and its surroundings accounts for the irreversibility of natural processes, often referred to in the concept of the arrow of time. The second law of thermodynamics allows the definition of the concept of thermodynamic temperature, but this has been formally delegated to the zeroth law of thermodynamics.

The first law of thermodynamics provides the definition of the internal energy of a thermodynamic system and expresses its change for a closed system in terms of work and heat. It can be linked to the law of conservation of energy. Conceptually, the first law describes the fundamental principle that systems do not consume or 'use up' energy, that energy is neither created nor destroyed, but is simply converted from one form to another. The second law is concerned with the direction of natural processes. It asserts that a natural process runs only in one sense and is not reversible. That is, the state of a natural system itself can be reversed, but not without increasing the entropy of the system's surroundings.

The German scientist Rudolf Clausius laid the foundation for the second law of thermodynamics in 1850 by examining the relation between heat transfer and work. His formulation of the second law, which was published in German in 1854, is known as the Clausius statement: "Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time." The statement by Clausius uses the concept of the ''passage of heat'. As is usual in thermodynamic discussions, this means the 'net transfer of energy as heat', and does not refer to contributory transfers one way and the other.

The second law is statistical, and there can always be minute violations in very small collections of particles. There is no practical application of this. For example, in 2002, researchers showed that on the level of thousands of atoms and molecules, fleeting energy increases violate the second law of thermodynamics. They found that over periods of less than two seconds, variations in the random thermal motion of water molecules occasionally gave individual beads a kick. This increased the beads' kinetic energy by a small but significant amount, in apparent violation of the second law.

The second law at the quantum level

The second law of thermodynamics is a physical law based on universal empirical observation concerning heat and energy interconversions. It establishes the concept of entropy as a physical property of a thermodynamic system. The second law is statistical in nature, and its reliability arises from the huge number of particles present in macroscopic systems.

At the quantum level, the second law is violated constantly, everywhere, and all the time. This is because the second law only applies to systems composed of many particles interacting. However, the laws of thermodynamics may also exist at the level of individual atoms. The second law of thermodynamics is a statement on the irreversibility of dynamics or the breakup of time-reversal symmetry (T-symmetry). This should be consistent with the empirical direct definition: heat will flow spontaneously from a hot source to a cold sink. From a static viewpoint, for a closed quantum system, the second law of thermodynamics is a consequence of the unitary evolution. In this approach, one accounts for the entropy change before and after a change in the entire system.

The second law of thermodynamics is also concerned with the direction of natural processes. It asserts that a natural process runs only in one sense and is not reversible. That is, the state of a natural system itself can be reversed, but not without increasing the entropy of the system's surroundings. The second law places constraints on state transformations. It applies to systems composed of many particles, and one can formulate laws of thermodynamics.

The second law for microscopic systems takes on a very different form than it does at the macroscopic scale, imposing not just one constraint on what state transformations are possible, but an entire family of constraints. These second laws are not only relevant for small systems but also apply to individual macroscopic systems interacting via long-range interactions, which only satisfy the ordinary second law on average. By making precise the definition of thermal operations, the laws of thermodynamics take on a form with the first law defining the class of thermal operations, the zeroth law emerging as a unique condition ensuring the theory is nontrivial, and the remaining laws falling into place.

The second law and the zeroth law of thermodynamics

The second law of thermodynamics is a physical law based on universal empirical observation concerning heat and energy interconversions. A simple statement of the law is that heat always flows spontaneously from hotter to colder regions of matter. The second law establishes the concept of entropy as a physical property of a thermodynamic system. It also allows the definition of the concept of thermodynamic temperature, but this has been formally delegated to the zeroth law of thermodynamics.

The second law of thermodynamics implies that equilibrium corresponds to the maximum total entropy, and that a system prepared in a non-equilibrium macrostate will move in the direction of increasing entropy. The second law also allows for the definition of the concept of thermodynamic temperature, but this has been formally delegated to the zeroth law of thermodynamics.

The zeroth law of thermodynamics states that if two bodies are each in thermal equilibrium with some third body, then they are also in thermal equilibrium with each other. This is important for the mathematical formulation of thermodynamics, which needs the assertion that the relation of thermal equilibrium is an equivalence relation. This information is needed for a mathematical definition of temperature that agrees with the physical existence of valid thermometers.

The zeroth law justifies the use of suitable thermodynamic systems as thermometers to provide such a labelling, which yields any number of possible empirical temperature scales. It also justifies the use of the second law of thermodynamics to provide an absolute, or thermodynamic, temperature scale. The zeroth law is needed for the definition of such scales, and justifies the use of practical thermometers.

The second law of thermodynamics is statistical, and there can always be minute violations in very small collections of particles. For example, in 2002, researchers showed that on the level of thousands of atoms and molecules, fleeting energy increases violate the second law of thermodynamics. Over periods of less than two seconds, variations in the random thermal motion of water molecules occasionally gave individual beads a kick, increasing their kinetic energy by a small but significant amount.

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