The concept of temperature is a central part of equilibrium thermodynamics and statistical mechanics: it is related to several thermodynamics’ laws, it is the key parameter of the equilibrium distribution, and even sets eﬃciency limitations to work extraction (Carnot bound). No wonder why so many have tried to extend the notion of temperatures to the realm of non-equilibrium systems.
This is achieved by defining an effective temperature, which is generally related to a violation of the fluctuation-dissipation theorem or the use of colored noise. The introduction of an effective temperature has helped reveal the nature of molecular motors in red-blood cell membranes, set bounds to the performance of active Brownian engines, study glasses, and more. Though in some cases the use of an effective temperature provides a good phenomenological description, the models used tend to either use unphysical assumptions such as negative friction or lack a microscopic model that could explain the physical nature of the disequilibrium and its thermodynamic repercussions.
We use the notion of effective temperatures for discovering the limitations that thermodynamics imposes on non-equilibrium systems. To achieve this, we are taking a unique approach and defining effective temperatures from a microscopic physical model. We have already shown that simple properties of these effective temperatures determine the thermodynamic capabilities of a non-equilibrium system. What else can the effective temperature tell us about non-equilibrium systems? For determining this we are studying the concept of effective temperatures in different systems.
Effective temperatures in quantum systems:
Quantum non-thermal baths:
An excellent review about the effective temperature:
An example of the application of effective temperature to study red-blood-cell: