## Nonequilibrium thermodynamics of stochastic systems with odd and even variables [1]

One and a half centuries after its introduction into science, the concept of entropy still has the capacity to mystify. In recent years some of the fog has begun to lift with the development of stochastic thermodynamics, a framework that fits into the familiar thermodynamic formulation of macroscopic objects, but extends to include the properties of nanosystems, where thermal fluctuations are significant. The stochastic production of entropy can be modelled for such systems, and it follows rules that differ from, and yet are consistent with the second law of thermodynamics.

__Professor Ian Ford__ [2] and Richard Spinney of the London Centre for Nanotechnology have shown that entropy production can usefully be divided into three components. The first two had been identified before and arise physically from relaxation (such as a system cooling down towards an ambient temperature) and from non-equilibrium constraints (such as contact with two heat baths at different temperatures) but the third is new and arises from both these causes acting together. Whilst the first two components are never negative on average, the average of the third component can take either sign: the sum of all three is never negative in accordance with the second law.

The new term allows us to treat the stochastic thermodynamics of small systems described by dynamics involving positions and velocities, in other words quite general situations. Some simple examples of systems undergoing stochastic dynamics, as illustrated by the Brownian motion of a trapped particle shown in the figure, have given us insight into the properties of the new component of entropy production, such that we can extend our understanding of the behaviour of nanosystems exposed to external mechanical and thermal forces.

**Journal link:** Phys. Rev. Lett. 108, 170603 (2012)__http://prl.aps.org/pdf/PRL/v108/i17/e170603__ [3]