Matrix product density operators: simulation of finite-temperature and dissipative systems

The equilibrium between a liquid and its vapor depends on the temperature of the system; a rise in temperature causes a corresponding rise in the vapor pressure of its liquid. The Clausius-Clapeyron equation gives the quantitative relation between a substance’s vapor pressure (P) and its temperature (T); it predicts the rate at which vapor pressure increases per unit increase in temperature.

For a system that undergoes a thermodynamic process at a constant volume condition, the heat absorbed is used only to increase the system's internal energy and not for doing any kind of work. While for a system undergoing a thermodynamic process under a constant pressure condition, the amount of heat absorbed is used not only for increasing the internal energy (as a function of temperature) but also for doing some work. The molar heat capacity is the amount of heat required to increase the...

The number of independent ways a gas molecule can move along straight line, rotate, and vibrate is called its degrees of freedom. Supposing d represents the number of degrees of freedom of an ideal gas, the molar heat capacity at constant volume of an ideal gas in terms of d is

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by

James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and Faraday.

The kinetic model of gases explains the properties of a perfect gas using three main assumptions: molecules move in ceaseless random motion, their size is negligible compared to the distances between them, and they do not interact except during perfectly elastic collisions. The total energy of a gas is the sum of the kinetic energies of all its constituent molecules. The pressure exerted by the gas arises from the continual bombardment of the container walls by billions of colliding molecules.