#### 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

Done