Statistical mechanics uses probability theory to determine how certain macroscopic physical systems behave.
Statistical mechanics is the name given to one of the branches that expands the scope and specializations of physics . It is an area of study that, appealing to probability theory , allows us to determine the behaviors both at the microscopic and macroscopic levels of a physical system .
With this discipline that gained momentum when knowledge in thermodynamics was consolidated, it is possible to make a description of multiple stochastic processes . When stopping at the beginnings and evolution of statistical mechanics, it is necessary to specifically mention three scientists thanks to their key contributions to giving momentum and strengthening to this subject: Ludwig Boltzmann , James Clerk Maxwell and Josiah Willard Gibbs .
Of them, the first is indicated as the main promoter of statistical mechanics from 1870 onwards. In addition to giving substance to the idea that addresses equilibrium within the framework of a statistical set and, by deducing the content of the proposal that is known as Boltzmann's equation , was the first to approach the essence of statistical mechanics of non-thermodynamic equilibrium . In 1884, on the other hand, his American colleague Gibbs exalted the concept of statistical mechanics, indicating that years ago it had been used for the first time by JC Maxwell . Around the years 1901/1902, a work by Gibbs called in Spanish “Elementary principles of statistical mechanics” became popular, offering a comprehensive approach to this discipline that is proposed there as ideal for addressing mechanical systems at micro and macroscopic scales.
Fundamentals, bases and scope of statistical mechanics
Statistical mechanics , as deduced from both theory and practice, transcends the universe of physics . This specialization that can be built from the laws that govern quantum mechanics and classical mechanics offers guidelines and resources that can be applied, for example, in the field of economics .
Statistical mechanics is even considered to analyze soft condensed matter, the dynamics of a natural ecosystem, how neural networks behave, the particularities of the thermodynamic equilibrium that involves an atom (which is characterized by presenting two sublevels). energy) and black body radiation.
Keeping in mind issues specific to statistical mechanics , it is also possible to deduce the laws of thermodynamics that influence the macroscopic behavior of gases. This occurs, to indicate two possibilities, with the so-called Boyle-Mariotte law (focused on the connection between the pressure and the volume of a certain amount of a gas that is maintained at a constant temperature) and the equation of state of an ideal gas. . It should be noted that when working with gases and trying to make a prediction about how they will behave, statistical mechanics emerges as an effective solution since it focuses on averages and not on individual particle performances. In this way, taking advantage of the mechanical laws and starting from a generic appreciation of the molecules that make up a certain gas, its thermodynamic properties can be deduced.
When the field of thermodynamics was consolidated, statistical mechanics received a great boost, a discipline that in turn has served to support the evolution of statistical physics.
Master the concepts of thermodynamics (a discipline that focuses, from a macroscopic perspective, on the state of thermodynamic equilibrium ), entropy (magnitude that marks the irreversibility in a thermodynamic system in equilibrium ) and Boltzmann's constant (value that links energy and absolute temperature ) is vital to know in detail the history of statistical mechanics as well as being aware of how they combine and complement each other in the statistical-thermodynamic relationship . At the same time, it must be taken into account that, currently, there are more practical groups of statistical assembly applied in statistical physics (a branch that uses information and methods specific to statistical mechanics ).
Quantum statistical mechanics
Within statistical mechanics there is a specialty that is applied to quantum systems .
In this field we work, to list some options, with the Von Neumann entropy and with the distinction between bosons and fermions . Regarding this last point, it is worth highlighting the importance of knowing the definitions of each one and of educating yourself about the theorem of the correspondence between spin and statistics , the Bose-Einstein statistics and the Fermi-Dirac statistics .
It is enriching to keep in mind, even, that ideas of quantum order began to develop at the level of statistical mechanics . Planck's constant , the idea of quantization , quantum entanglement and Bohr's atomic model , for example, were born and gained relevance over time.
Much has already been learned about statistical mechanics, but this discipline continues to be an object of study and is used in numerous areas to investigate the most varied topics.
It is also interesting to dwell on quantum field theory and its role in the resolution of the Ising model . This structure, a physical model that Wilhelm Lenz developed when Ernst Ising , one of his students, was investigating ferromagnetism , is a paradigmatic unit within statistical mechanics , where at the time the fact of phase transitions that is present was controversial. in said model.