flow of energy across the boundaries of the system due to the corresponding conjugate pair. These concepts will be expanded upon in the following sections. While dealing with processes in which systems exchange matter or energy, classical thermodynamics is not concerned with the rate at which such processes take place, termed kinetics. For this reason, the term thermodynamics is usually used synonymously with equilibrium thermodynamics. A central notion for this connection is that of quasistatic processes, namely idealized, "infinitely slow" processes. Time-dependent thermodynamic processes far away from equilibrium are studied by non-equilibrium thermodynamics. This can be done through linear or non-linear analysis of irreversible processes, allowing systems near and far away from equilibrium to be studied, respectively. Pressure/volume and stress/strain pairs As an example, consider the conjugate pair. The pressure acts as a generalized force – pressure differences force a change in volume, and their product is the energy lost by the system due to mechanical work. Pressure is the driving force, volume is the associated displacement, and the two form a pair of conjugate variables. The above holds true only for non-viscous fluids. In the case of viscous fluids, plastic and elastic solids, the pressure force is generalized to the stress tensor, and changes in volume are generalized to the volume multiplied by the strain tensor. These then form a conjugate pair. If is the ij component of the stress tensor, and is the ij component of the strain tensor, then the mechanical work done as the result of a stress-induced infinitesimal strain is: or, using Einstein notation for the tensors, in which repeated indices are assumed to be summed: In the case of pure compression (i.e. no shearing forces), the stress tensor is simply the negative of the pressure times the unit tensor so that The trace of the strain tensor () is the fractional change in volume so that the above reduces to as it should. Temperature/entropy pair In a similar way, temperature differences drive changes in entropy, and their product is the energy transferred by heating. Temperature is the driving force, entropy is the associated displacement, and the two form a pair of conjugate variables. The temperature/entropy pair of conjugate variables is the only heat term; the other terms are essentially all various forms of work. Chemical potential/particle number pair The chemical potential is like a force which pushes an increase in particle number. In cases