I've studied "Markov Chains" - Norris and "Measure, Integral and Probability" - Capinski, Kopp. Now, I'm looking for a couple of books (or other references) that help me bridging these two topics. More precisely I'm looking for something that:

1. does a parallelism between the probability of a markov chain, as defined in basic textbooks, with the measure theory counterpart (and the same for other quantities), thus explaining how to go from one to the other

2. shows a possible definition of thermodynamic quantities (such as heat and entropy) in terms of a stochastic process

Thanks for your help!

p.s. this question was taken in part from here

I've studied "Markov Chains" - Norris and "Measure, Integral and Probability" - Capinski, Kopp. Now, I'm looking for a couple of books (or other references) that help me bridging these two topics. More precisely I'm looking for something that:

1. does a parallelism between the probability of a markov chain, as defined in basic textbooks, with the measure theory counterpart (and the same for other quantities), thus explaining how to go from one to the other

2. shows a possible definition of thermodynamic quantities (such as heat and entropy) in terms of a stochastic process

Thanks for your help!

p.s. this question was taken in part from here