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Thermodynamics & Statistical Mechanics
46 flashcards
The first law states that energy can be converted from one form to another, but it cannot be created or destroyed. The total energy of an isolated system remains constant.
The second law states that the total entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.
Entropy is a measure of the disorder or randomness of a system. It quantifies how much energy in a system is unavailable to do useful work.
The third law states that as a system approaches absolute zero, its entropy approaches a constant value, which is typically very small.
A reversible process is one that can be reversed without any change occurring in the surroundings. An irreversible process is one that cannot be reversed without some change occurring in the surroundings.
The Boltzmann distribution describes the probability distribution of a system over its possible states as a function of temperature and energy.
Entropy and information are closely related concepts. Entropy is a measure of the disorder or randomness in a system, while information is a measure of the order or pattern in a system.
Heat is the transfer of energy due to a temperature difference, while work is the transfer of energy due to a force acting through a displacement.
The Carnot cycle is an idealized thermodynamic cycle that describes the most efficient way to convert heat into work, or vice versa, between a hot and a cold reservoir.
The ideal gas law relates the pressure, volume, amount of substance, and absolute temperature of an ideal gas through the equation PV = nRT.
A microstate is a specific configuration of a system at the molecular level, while a macrostate is a collective property of a system that can be described by macroscopic variables like temperature, pressure, and volume.
The Boltzmann constant is a physical constant that relates the average kinetic energy of particles in a gas to the absolute temperature of the gas.
The Helmholtz free energy is a thermodynamic quantity that measures the useful work obtainable from a closed system at constant temperature and volume.
The Gibbs free energy is a thermodynamic quantity that measures the useful work obtainable from a closed system at constant temperature and pressure.
A closed system is one that does not exchange matter with its surroundings, but can exchange energy. An open system can exchange both matter and energy with its surroundings.
The zeroth law states that if two systems are in thermal equilibrium with a third system, they must also be in thermal equilibrium with each other.
An isothermal process occurs at constant temperature, while an adiabatic process occurs without any transfer of heat to or from the surroundings.
The Clausius inequality states that the integral of the quantity dQ/T, taken around a complete cycle, is always less than or equal to zero for any cyclic process.
Classical mechanics treats matter as continuous and deterministic, while quantum mechanics treats matter as discrete and probabilistic, governed by the principles of quantum theory.
The Fermi-Dirac distribution describes the statistical behavior of fermions, particles with half-integer spin, in a system.
The Bose-Einstein distribution describes the statistical behavior of bosons, particles with integer spin, in a system.
The partition function is a fundamental quantity in statistical mechanics that encodes the statistical properties of a system in thermodynamic equilibrium.
A canonical ensemble describes a system with a fixed number of particles, volume, and temperature, while a grand canonical ensemble describes a system with a fixed chemical potential, volume, and temperature.
The principle of maximum entropy production states that a system will naturally evolve towards a state that maximizes the rate of entropy production, subject to any constraints on the system.
The Onsager reciprocal relations relate the flow of thermodynamic forces and fluxes in a system that is close to equilibrium, and state that certain coefficients relating these quantities are equal.
The fluctuation-dissipation theorem relates the fluctuations in a system near equilibrium to the dissipative processes that occur when the system is perturbed from equilibrium.
The equipartition theorem states that, in a system in thermal equilibrium, the total kinetic and potential energy is equally partitioned among all the degrees of freedom of the system.
The virial theorem relates the average kinetic energy of a system of particles to the average potential energy of the system, and is useful in the study of the behavior of gases, stars, and other systems.
The van der Waals equation of state is an improvement over the ideal gas law that accounts for the finite size of molecules and the attractive forces between them.
The Debye model is a theoretical model that describes the vibrational properties of solids by treating them as a collection of quantized harmonic oscillators.
The Einstein model is a theoretical model that describes the vibrational properties of solids by treating them as a collection of independent quantum harmonic oscillators.
A Bravais lattice is an abstract concept that describes the periodic arrangement of points in space, while a crystal structure is a specific arrangement of atoms or molecules in a solid material.
Fermions are particles with half-integer spin that obey the Pauli exclusion principle, while bosons are particles with integer spin that can occupy the same quantum state.
A classical gas is described by classical mechanics and obeys the laws of classical thermodynamics, while a quantum gas is described by quantum mechanics and exhibits quantum effects like particle statistics and energy quantization.
Bose-Einstein condensation is a state of matter that occurs when a gas of bosons is cooled to very low temperatures, and a large fraction of the particles occupies the lowest quantum state.
Paramagnetic materials are weakly attracted to an external magnetic field due to the presence of unpaired electrons, while diamagnetic materials are weakly repelled by an external magnetic field due to the motion of paired electrons.
The Curie-Weiss law describes the temperature dependence of the magnetic susceptibility of a paramagnetic material.
The Ising model is a mathematical model of ferromagnetism that describes the behavior of a system of spins on a lattice, and is widely used in the study of phase transitions and critical phenomena.
The Landau theory is a phenomenological theory that describes phase transitions and the behavior of systems near critical points using an order parameter and a free energy expansion.
A first-order phase transition involves a discontinuous change in the first derivative of the free energy with respect to a thermodynamic variable, while a second-order phase transition involves a discontinuous change in the second derivative.
The renormalization group theory is a mathematical tool used to study the behavior of systems at different length scales and to understand critical phenomena and phase transitions.
The Jarzynski equality is a mathematical relation that relates the free energy difference between two equilibrium states to the work done on the system during a non-equilibrium process.
A classical heat engine operates according to the principles of classical thermodynamics, while a quantum heat engine operates according to the principles of quantum thermodynamics and can exploit quantum effects like coherence and entanglement.
The Wigner function is a quasi-probability distribution function that provides a phase-space representation of a quantum mechanical state, and is useful in the study of quantum statistical mechanics.
A Fermi liquid is a theoretical model that describes the behavior of interacting fermions in a metal, while a Luttinger liquid is a theoretical model that describes the behavior of interacting fermions in one-dimensional systems.
The Mermin-Wagner theorem states that continuous symmetries cannot be spontaneously broken in systems with sufficiently short-range interactions in dimensions less than or equal to two.