The Gibbs distribution, also known as the Boltzmann distribution, describes the probability of a system being in a certain state as a function of that state's energy and temperature, fundamental to statistical mechanics. It provides a bridge between microscopic properties of particles and macroscopic observables, essential for understanding thermodynamic equilibrium and phase transitions.

Gibbs Distribution

Gibbs distribution

The Boltzmann Distribution describes the distribution of energy states among particles in a system at thermal equilibrium, indicating that lower energy states are more likely to be occupied than higher ones. It is fundamental in statistical mechanics and helps explain phenomena like temperature dependence of reaction rates and population of quantum states.

Boltzmann distribution

probability of a system

certain state

Function of energy

Function of temperature

Statistical mechanics is a branch of physics that uses probability theory to study and predict the behavior of systems with a large number of particles, bridging the microscopic laws of physics with macroscopic observations. It provides the framework for understanding thermodynamic properties and phase transitions by averaging over the possible states of a system rather than tracking individual particles.

statistical mechanics

microscopic properties of particles

macroscopic observables

Thermodynamic equilibrium is a state where a system's macroscopic properties remain constant over time, with no net flow of energy or matter. It implies that the system is in thermal, mechanical, and chemical equilibrium, ensuring uniform temperature, pressure, and chemical potential throughout.

thermodynamic equilibrium

Phase transitions are transformations between different states of matter, such as solid, liquid, and gas, characterized by abrupt changes in physical properties. These transitions occur at specific conditions of temperature and pressure, and are often associated with critical phenomena and symmetry breaking.

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