fázisterét

A fázisterét, or phase space, is a mathematical construct used in physics, particularly in statistical mechanics and Hamiltonian mechanics, to describe the state of a dynamic system. It is a multidimensional space where each dimension represents a generalized coordinate or momentum of the system. For a system with *n* degrees of freedom, its phase space will have *2n* dimensions, with *n* dimensions for the generalized coordinates and *n* dimensions for the corresponding generalized momenta.

The position of a point in phase space uniquely defines the complete state of the system at a given instant. As the system evolves over time, this point traces a trajectory within the phase space. The laws of physics dictate the movement of this point, and the collection of all possible trajectories represents the dynamics of the system.

In Hamiltonian mechanics, the evolution of a system in phase space is governed by Hamilton's equations. These equations describe how the coordinates and momenta change over time, thus defining the trajectory. For conservative systems, the total energy, represented by the Hamiltonian, remains constant along any given trajectory.

The concept of phase space is crucial for understanding the behavior of systems with a large number of particles, such as gases. Statistical mechanics uses phase space to average over all possible microstates of a system to predict macroscopic properties. The volume of a region in phase space is directly related to the number of accessible microstates. Liouville's theorem is a fundamental result in this context, stating that the volume of a region in phase space occupied by a system of non-interacting particles remains constant over time. This theorem has significant implications for the reversibility of dynamical processes and the foundations of statistical mechanics.