6dTEMP

6dTemp is a theoretical framework for representing temperature in six dimensions, designed to describe anisotropic energy distributions in non-equilibrium systems. It replaces the traditional single scalar temperature with a six-component temperature vector, capturing different modes and directions of energy flow.

The six components are grouped into three translational and three rotational terms, forming T6d = (T_tr_x, T_tr_y, T_tr_z, T_rot_x, T_rot_y, T_rot_z). In equilibrium, these components converge to a common scalar T, recovering the familiar notion of temperature. The framework provides a metric to quantify distances between states in six-dimensional temperature space and relates each component to a corresponding portion of the kinetic energy.

Estimation of the components can be performed from molecular dynamics simulations, spectroscopy data, or other kinetic measurements by computing ensemble averages of translational velocities and rotational motions. Statistical methods, including Bayesian inference, may be used to infer component uncertainties when data are sparse or noisy.

Applications include non-equilibrium molecular dynamics, plasma physics, and materials science under strong fields or rapid heating, where directional energy distribution matters. The concept serves as a descriptive tool rather than a directly observable quantity, assisting in interpreting energy transfer pathways and thermalization processes.

Limitations include dependence on the chosen degrees of freedom and the underlying model, potential ambiguity in separating modes, and the challenge of validating six independent components against experimental data. See also temperature, anisotropic temperature, non-equilibrium thermodynamics, molecular dynamics.