Second law of thermodynamics in the context of "Dissipation"

The species–area relationship or species–area curve describes the relationship between the area of a habitat, or of part of a habitat, and the number of species found within that area. Larger areas tend to contain larger numbers of species, and empirically, the relative numbers seem to follow systematic mathematical relationships. The species–area relationship is usually constructed for a single type of organism, such as all vascular plants or all species of a specific trophic level within a particular site. It is rarely if ever, constructed for all types of organisms if simply because of the prodigious data requirements. It is related but not identical to the species discovery curve.

Ecologists have proposed a wide range of factors determining the slope and elevation of the species–area relationship. These factors include the relative balance between immigration and extinction, rate and magnitude of disturbance on small vs. large areas, predator-prey dynamics, and clustering of individuals of the same species as a result of dispersal limitation or habitat heterogeneity. The species–area relationship has been reputed to follow from the 2nd law of thermodynamics. In contrast to these "mechanistic" explanations, others assert the need to test whether the pattern is simply the result of a random sampling process. Species–area relationships are often evaluated in conservation science in order to predict extinction rates in the case of habitat loss and habitat fragmentation.

In thermodynamics, an irreversible process is a process that cannot be undone. All complex natural processes are irreversible, although a phase transition at the coexistence temperature (e.g. melting of ice cubes in water) is well approximated as reversible.

A change in the thermodynamic state of a system and all of its surroundings cannot be precisely restored to its initial state by infinitesimal changes in some property of the system without expenditure of energy. A system that undergoes an irreversible process may still be capable of returning to its initial state. Because entropy is a state function, the change in entropy of the system is the same whether the process is reversible or irreversible. However, the impossibility occurs in restoring the environment to its own initial conditions. An irreversible process increases the total entropy of the system and its surroundings. The second law of thermodynamics can be used to determine whether a hypothetical process is reversible or not.

Entropy is a scientific concept, most commonly associated with states of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, and information systems including the transmission of information in telecommunication.

Entropy is central to the second law of thermodynamics, which states that the entropy of an isolated system left to spontaneous evolution cannot decrease with time. As a result, isolated systems evolve toward thermodynamic equilibrium, where the entropy is highest. "High" entropy means that energy is more disordered or dispersed, while "low" entropy means that energy is more ordered or concentrated. A consequence of the second law of thermodynamics is that certain processes are irreversible.

Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics, which convey a quantitative description using measurable macroscopic physical quantities but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to various topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering, and mechanical engineering, as well as other complex fields such as meteorology.

Historically, thermodynamics developed out of a desire to increase the efficiency of early steam engines, particularly through the work of French physicist Sadi Carnot (1824) who believed that engine efficiency was the key that could help France win the Napoleonic Wars. Scots-Irish physicist Lord Kelvin was the first to formulate a concise definition of thermodynamics in 1854 which stated, "Thermo-dynamics is the subject of the relation of heat to forces acting between contiguous parts of bodies, and the relation of heat to electrical agency." German physicist and mathematician Rudolf Clausius restated Carnot's principle known as the Carnot cycle and gave the theory of heat a truer and sounder basis. His most important paper, "On the Moving Force of Heat", published in 1850, first stated the second law of thermodynamics. In 1865 he introduced the concept of entropy. In 1870 he introduced the virial theorem, which applied to heat.

Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass of differing chemical species (mass transfer in the form of advection), either cold or hot, to achieve heat transfer. While these mechanisms have distinct characteristics, they often occur simultaneously in the same system.

Heat conduction, also called diffusion, is the direct microscopic exchanges of kinetic energy of particles (such as molecules) or quasiparticles (such as lattice waves) through the boundary between two systems. When an object is at a different temperature from another body or its surroundings, heat flows so that the body and the surroundings reach the same temperature, at which point they are in thermal equilibrium. Such spontaneous heat transfer always occurs from a region of high temperature to another region of lower temperature, as described in the second law of thermodynamics.

A supersonic expansion fan, technically known as Prandtl–Meyer expansion fan, a two-dimensional simple wave, is a centered expansion process that occurs when a supersonic flow turns around a convex corner. The fan consists of an infinite number of Mach waves, diverging from a sharp corner. When a flow turns around a smooth and circular corner, these waves can be extended backwards to meet at a point.

Each wave in the expansion fan turns the flow gradually (in small steps). It is physically impossible for the flow to turn through a single "shock" wave because this would violate the second law of thermodynamics.

Ludwig Eduard Boltzmann (/ˈbɔːltsˌmɑːn/ BAWLTS-mahn or /ˈboʊltsmən/ BOHLTS-muhn; German: [ˈluːtvɪç ˈeːduaʁt ˈbɔltsman]; 20 February 1844 – 5 September 1906) was an Austrian mathematician and theoretical physicist. His greatest achievements were the development of statistical mechanics and the statistical explanation of the second law of thermodynamics. In 1877 he provided the current definition of entropy, ${\displaystyle S=k_{\rm {B}}\ln \Omega }$, where Ω is the number of microstates whose energy equals the system's energy, interpreted as a measure of the statistical disorder of a system. Max Planck named the constant k_B the Boltzmann constant.

Statistical mechanics is one of the pillars of modern physics. It describes how macroscopic observations (such as temperature and pressure) are related to microscopic parameters that fluctuate around an average. It connects thermodynamic quantities (such as heat capacity) to microscopic behavior, whereas, in classical thermodynamics, the only available option would be to measure and tabulate such quantities for various materials.