Room 117

Fluctuating States: What is the Probability of a Thermodynamical Transition?

Tanmay Saha

IMSc

If the second law of thermodynamics forbids a transition
from one state to another, then it is still possible to make the
transition happen by using a sufficient amount of work. But if we do
not have access to this amount of work, can the transition happen
probabilistically? In the thermodynamic limit, this probability
tends to zero, but here we find that for finite-sized and quantum
systems it can be finite. We compute the
maximum probability of a transition or a thermodynamical fluctuation
from any initial state to any final
state and show that this maximum can be achieved for any final state
that is block diagonal in the energy eigenbasis. We also find upper
and lower bounds on this transition probability, in terms of the work of
transition. As a by-product, we introduce a finite set of
thermodynamical monotones related to the
thermomajorization criteria which governs state transitions and
compute the work of transition in terms of
them. The trade-off between the probability of a transition and any
partial work added to aid in that
transition is also considered. Our results have applications in
entanglement theory, and we find the amount
of entanglement required (or gained) when transforming one pure
entangled state into any other.

Link:journals.aps.org/prx/pdf/10.1103/PhysRevX.6.041016