"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."
A measure of the disorder or randomness of a system.
Thermodynamics: The study of the relationship between energy and its transformations in systems, including the laws of thermodynamics.
Statistical mechanics: A branch of physics that uses the principles of probability and statistics to describe the behavior of large systems of particles.
Boltzmann's formula: A mathematical formula that expresses the relationship between entropy, temperature, and the number of microstates available to a system.
Microstates and macrostates: Microstates are the different configurations that a system can take, while macrostates are the overall states of the system that can be observed.
The Second Law of Thermodynamics: A principle that states that the total entropy of a closed or isolated system cannot decrease over time.
Heat engines: Devices that convert thermal energy into mechanical work, working on the principle of the Second Law of Thermodynamics.
Reversible and irreversible processes: Reversible processes can be reversed with minimal energy input, while irreversible processes cannot.
Maxwell's demon: A thought experiment in which a hypothetical demon manipulates the distribution of particles in a gas to decrease the entropy of the system.
Information theory and entropy: The relationship between information and entropy in communication systems, where entropy represents the uncertainty or randomness of a message.
Black holes and entropy: The relationship between black holes and the entropy of their surrounding space, leading to the concept of the holographic principle.
Quantum mechanics and entropy: The application of quantum mechanics to the study of entropy in small-scale systems, leading to the development of quantum information theory.
Entropy in biological systems: The role of entropy in biological systems, including the organization of living systems and the concept of biological information.
Thermodynamic entropy: Thermodynamic entropy is a measure of the degree of randomness or disorder in a system. It is a macroscopic quantity that is related to the number of ways that the constituents of a system can be arranged within the system.
Statistical entropy: Statistical entropy is a measure of the number of ways that the particles in a system can be arranged, given their position and energy. It is a microscopic quantity that is related to the number of possible states that the system can take on.
"He defined it as the quotient of an infinitesimal amount of heat to the instantaneous temperature."
"Later coined the term entropy from a Greek word for transformation."
"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."
"Austrian physicist Ludwig Boltzmann explained entropy as the measure of the number of possible microscopic arrangements or states of individual atoms and molecules of a system that comply with the macroscopic condition of the system."
"He thereby introduced the concept of statistical disorder and probability distributions into a new field of thermodynamics, called statistical mechanics."
"...a proportionality constant, the Boltzmann constant, that has become one of the defining universal constants..."
"In 1948, Bell Labs scientist Claude Shannon developed similar statistical concepts..."
"...measuring microscopic uncertainty and multiplicity to the problem of random losses of information in telecommunication signals."
"Upon John von Neumann's suggestion, Shannon named this entity of missing information in analogous manner to its use in statistical mechanics as entropy, and gave birth to the field of information theory."
"...the transmission of information in telecommunication."
"...interpret[ing] the concept as meaning disgregation."
"The thermodynamic concept was referred to by Scottish scientist and engineer William Rankine in 1850 with the names thermodynamic function and heat-potential."
"It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change, and information systems..."
"He initially described it as transformation-content, in German Verwandlungsinhalt..."
"Austrian physicist Ludwig Boltzmann explained entropy as the measure of the number of possible microscopic arrangements or states of individual atoms and molecules of a system that comply with the macroscopic condition of the system."
"A consequence of the second law of thermodynamics is that certain processes are irreversible."
"...and later coined the term entropy from a Greek word for transformation."
"...Shannon named this entity of missing information in analogous manner to its use in statistical mechanics as entropy."