Systems are in thermal equilibrium when no net heat flows between them; their temperatures are equal.
In static thermal equilibrium, the local temperature times the stationary lapse is constant. Energy measured locally redshifts to conserved Killing energy by that same lapse; requiring a single equilibrium Boltzmann exponent gives the relation. The Killing vector field normalization fixes the constant but not the ratio of temperatures at different locations.
Boltzmann suppression is the exponential reduction of an equilibrium population when creating it costs energy much greater than the temperature. For a nonrelativistic species with negligible chemical potential, the leading factor is , multiplied by its momentum phase-space volume. It concerns the equilibrium abundance; freeze-out can preserve a larger population than the instantaneous equilibrium value at later times.
A nonrelativistic species with states and negligible chemical potential has equilibrium density . If particle-antiparticle annihilation maintains equilibrium after the species becomes massive, its eventual freeze-out population can be much smaller than a relativistically decoupled population. The nonrelativistic annihilation rate and any asymmetry determine the final abundance.
Momentum-exchange collisions maintain a common temperature and an equilibrium-shaped momentum probability distribution. Particle abundances and chemical potentials need not have their chemical equilibrium values: elastic scattering alone conserves particle number. Thus kinetic equilibrium does not by itself imply either zero chemical potential or conserved comoving entropy.
A heat bath, or thermal reservoir, is an idealized system so large that exchanging a finite amount of heat does not appreciably change its temperature.
If two otherwise isolated systems freely exchange energy while remains fixed, their total entropy isAt an interior maximum, . Since thermodynamic temperature satisfies , the systems have equal temperatures at thermal equilibrium.
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Thermal equilibrium refers to a condition in which two or more objects or systems exchanged heat until they reach the same temperature, resulting in no net flow of thermal energy between them. At thermal equilibrium, the temperature of the objects remains constant over time because the energy they exchange is balanced.