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Writing Invariants For POJOs That Validate Business Rules

I want to start incorporating the practice of writing invariants for my classes. For my POJOs, is it a good practice to validate its state by validating it against business rules. Say I have
this class for instance:
#Data
public class Pick {
List<Substitution> substitutions = new ArrayList<>();
}
Now, my invariant says that every substitution object in the list needs to have a substitution reason. Is it a good practice to do such business checks inside POJOs that are meant to be simple data carriers?
Note that I already use #NonNull which is also an invariant, although a very basic one. Is it a good practice to write invariants that test for complex business relationships b/w your fields?

JSR 380 is a specification of the Java API for bean validation, part of Jakarta EE and JavaSE, which ensures that the properties of a bean meet specific criteria, using annotations such as #NotNull, #Min, and #Max.
We can see this approach used in Java ecosystem heavily, as far as it doesn't touch your business logic and also data object and keeps them clean it is goof
more here

Naming of classes in an adapter API

I am working on a Java library which wraps an existing general purpose API in a more specialized, servlet aware API. The wrapper API consists of exact same classes as the unerlying API, but some method signatures are re-written in terms of servlet objects, like HttpServletRequest. The original developer followed the naming convention of prepending the word Servlet to the existing class name, e.g. Connection in the existing API becomes ServletConnection and Session becomes ServletSession. Is this naming a good idea, or should the classes have the same names? My question may seem a matter of taste, but I am hoping for answers based on reason. The Scala collections API, for instance, reuses class names between mutable and immutable collections.

Confuse among JavaBeans, POJO, beans?

As far as I know, JavaBeans are the simple getter and setters methods of whatever fields are there in your Java class, on the other hand POJO seems similar (fields and its getter/setter) whats the difference then?
As that's not enough, here comes the beans floating around in all your JSPs and Struts config files, does (according to my knowledge) same stuff...
I am confuse by naming, whats the difference, what are the magic words?
Why do they call it bean, what should I say, if any one ask me describe bean in context of Java EE / JSP / Struts.

A POJO is a plain java object that doesn't adhere to any framework standard. Often Java Beans are considered POJOs as well, since the Java Beans Standard (or what is used of it) is kind of weak.
Java Beans are Java classes that adhere to certain naming conventions (mainly the getter setter thing) and are used in many contexts. JSPs is one of them. There is actually more to Java Bean then most people use. You can learn about it in this tutorial: http://docs.oracle.com/javase/tutorial/javabeans/index.html
Why is it called bean? I can only guess: Java -> Coffee -> Bean on one hand and on the other hand a bean is something simple, self contained which is kind of appropriate for a 'component'

A JavaBean is a POJO that is serializable, has a no-argument constructor, and allows access to properties using getter and setter methods. An Enterprise JavaBean is not a single class but an entire component model (again, EJB 3 reduces the complexity of Enterprise JavaBeans).
So main difference that could be seen is POJOs can be more encapsulated - have argument constructors and throw away some setters that should be used only once per object. JavaBean as you mentioned enforces some strick standard which isn't the best solution to every need.

What is meaning of Plain Old Java Object (POJO)?

What does the term Plain Old Java Object (POJO) mean? I couldn't find anything explanatory enough.
POJO's Wikipedia page says that POJO is an ordinary Java Object and not a special object. Now, what makes or what doesn't make and object special in Java?
The above page also says that a POJO should not have to extend prespecified classes, implement prespecified Interfaces or contain prespecified Annotations. Does that also mean that POJOs are not allowed to implement interfaces like Serializable, Comparable or classes like Applets or any other user-written Class/Interfaces?
Also, does the above policy (no extending, no implementing) means that we are not allowed to use any external libraries?
Where exactly are POJOs used?
EDIT: To be more specific, am I allowed to extend/implement classes/interfaces that are part of the Java or any external libraries?

Plain Old Java Object The name is used to emphasize that a given object is an ordinary Java Object, not a special object such as those defined by the EJB 2 framework.
class A {}
class B extends/implements C {}
Note: B is non POJO when C is kind of distributed framework class or ifc.
e.g. javax.servlet.http.HttpServlet, javax.ejb.EntityBean or J2EE extn
and not serializable/comparable. Since serializable/comparable are valid for POJO.
Here A is simple object which is independent.
B is a Special obj since B is extending/implementing C. So B object gets some more meaning from C and B is restrictive to follow the rules from C. and B is tightly coupled with distributed framework. Hence B object is not POJO from its definition.
Code using class A object reference does not have to know anything about the type of it, and It can be used with many frameworks.
So a POJO should not have to 1) extend prespecified classes and 2) Implement prespecified interfaces.
JavaBean is a example of POJO that is serializable, has a no-argument constructor, and allows access to properties using getter and setter methods that follow a simple naming convention.
POJO purely focuses on business logic and has no dependencies on (enterprise) frameworks.
It means it has the code for business logic but how this instance is created, Which service(EJB..) this object belongs to and what are its special characteristics( Stateful/Stateless) it has will be decided by the frameworks by using external xml file.
Example 1: JAXB is the service to represent java object as XML; These java objects are simple and come up with default constructor getters and setters.
Example 2: Hibernate where simple java class will be used to represent a Table. columns will be its instances.
Example 3: REST services. In REST services we will have Service Layer and Dao Layer to perform some operations over DB. So Dao will have vendor specific queries and operations. Service Layer will be responsible to call Which DAO layer to perform DB operations. Create or Update API(methods) of DAO will be take POJOs as arguments, and update that POJOs and insert/update in to DB. These POJOs (Java class) will have only states(instance variables) of each column and its getters and setters.
In practice, some people find annotations elegant, while they see XML as verbose, ugly and hard to maintain, yet others find annotations pollute the POJO model.
Thus, as an alternative to XML, many frameworks (e.g. Spring, EJB and JPA) allow annotations to be used instead or in addition to XML:
Advantages:
Decoupling the application code from the infrastructure frameworks is one of the many benefits of using POJOs. Using POJOs future proofs your application's business logic by decoupling it from volatile, constantly evolving infrastructure frameworks. Upgrading to a new version or switching to a different framework becomes easier and less risky. POJOs also make testing easier, which simplifies and accelerates development. Your business logic will be clearer and simpler because it won't be tangled with the infrastructure code
References : wiki source2

According to Martin Fowler, he and some others came up with it as a way to describe something which was a standard class as opposed to an EJB etc.

Usage of the term implies what it's supposed to tell you. If, for example, a dependency injection framework tells you that you can inject a POJO into any other POJO they want to say that you do not have to do anything special: there is no need to obey any contracts with your object, implement any interfaces or extend special classes. You can just use whatever you've already got.
UPDATE To give another example: while Hibernate can map any POJO (any object you created) to SQL tables, in Core Data (Objective C on the iPhone) your objects have to extend NSManagedObject in order for the system to be able to persist them to a database. In that sense, Core Data cannot work with any POJO (or rather POOCO=PlainOldObjectiveCObject) while Hibernate can. (I might not by 100% correct re Core Data since I just started picking it up. Any hints / corrections are welcome :-) ).

Plain Old Java Object :)
Well, you make it sound like those are all terrible restrictions.
In the usual context where POJO is/are used, it's more like a benefit:
It means that whatever library/API you're working with is perfectly willing to work with Java objects that haven't been doctored or manhandled in any way, i.e. you don't have to do anything special to get them to work.
For example, the XStream XML processor will (I think) happily serialize Java classes that don't implement the Serializable interface. That's a plus! Many products that work with data objects used to force you to implement SomeProprietaryDataObject or even extend an AbstractProprietaryDataObject class. Many libraries will expect bean behavior, i.e. getters and setters.
Usually, whatever works with POJOs will also work with not-so-PO-JO's. So XStream will of course also serialize Serializable classes.

POJO is a Plain Old Java Object - as compared to something needing Enterprise Edition's (J2EE) stuff (beans etc...).
POJO is not really a hard-and-fast definition, and more of a hand-wavy way of describing "normal" non-enterprise Java Objects. Whether using an external library or framework makes an object POJO or not is kind of in the eye of the beholder, largely depending on WHAT library/framework, although I'd venture to guess that a framework would make something less of a POJO

The whole point of a POJO is simplicity and you appear to be assuming its something more complicated than it appears.
If a library supports a POJO, it implies an object of any class is acceptible. It doesn't mean the POJO cannot have annotations/interface or that they won't be used if they are there, but it is not a requirement.
IMHO The wiki-page is fairly clear. It doesn't say a POJO cannot have annotations/interfaces.

What does the term Plain Old Java Object (POJO) mean?
POJO was coined by Martin Fowler, Rebecca Parsons and Josh Mackenzie when they were preparing for a talk at a conference in September 2000. Martin Fowler in Patterns of Enterprise Application Architecture explains how to implement a Domain Model pattern in Java. After enumerating some of disadvantages of using EJB Entity Beans:
There's always a lot of heat generated when people talk about
developing a Domain Model in J2EE. Many of the teaching materials and
introductory J2EE books suggest that you use entity beans to develop a
domain model, but there are some serious problems with this approach,
at least with the current (2.0) specification.
Entity beans are most useful when you use Container Managed
Persistence (CMP)...
Entity beans can't be re-entrant. That is, if you call out from one
entity bean into another object, that other object (or any object it
calls) can't call back into the first entity bean...
...If you have remote objects with fine-grained interfaces you get
terrible performance...
To run with entity beans you need a container and a database
connected. This will increase build times and also increase the time
to do test runs since the tests have to execute against a database.
Entity beans are also tricky to debug.
As an alternative, he proposed to use Regular Java Objects for Domain Model implementation:
The alternative is to use normal Java objects, although this often
causes a surprised reaction—it's amazing how many people think that
you can't run regular Java objects in an EJB container. I've come to
the conclusion that people forget about regular Java objects because
they haven't got a fancy name. That's why, while preparing for a talk
in 2000, Rebecca Parsons, Josh Mackenzie, and I gave them one: POJOs
(plain old Java objects). A POJO domain model is easy to put together,
is quick to build, can run and test outside an EJB container, and is
independent of EJB (maybe that's why EJB vendors don't encourage you
to use them).

There is an abundance of posts that are half correct and half incorrect. The best example of the correct interpretation is given by Rex M in their answer here.
[POJO are classes] that doesn't require any significant "guts" to make
it work. The idea is in contrast with very dependent objects that have
a hard time being (or can't be) instantiated and manipulated on their
own - they require other services, drivers, provider instances, etc.
to also be present.
Unfortunately, these very same answers often come along with the misunderstanding that they are somehow simple or often have a simple structure. This is not necessarily true and the confusion seems to stem from the fact that in the Java (POJO) and C# world (POCO) business logic is relatively easily modeled especially in the web application world.
POJO's can have multiple levels of inheritance, generic types, abstractions, etc. It just so happens that this isn't required in the majority of web applications as business logic doesn't necessitate it - alot of the effort goes into databases, queries, data transfer objects and repositories.
As soon as you step out of line with simple web apps, your POJO's start looking a lot more complex. E.g. Make a web app that assigns taxi's to user schedules. To do this, you need a graph coloring algorithm. To color the graphs, you need a graph object. Each node in the graph is a schedule object. Now what if we want to make it generic so that coloring the graph can be done not only with schedules but other things as well. We can make it generic, abstract and add levels of inheritance - almost to the point of making it a mini library.
At this point though, no matter its complexity, its still a POJO because it doesn't rely on the guts of other frameworks.

A Plain Old Java Object (POJO) that contains all of the business logic for your extension.
Exp. Pojo which contains a single method
public class Extension {
public static void logInfo(String message) {
System.out.println(message);
}
}

Is implementing java.io.Serializable even in simple POJO Java classes a best practice?

In general, is it a best practice to have simple POJO Java classes implement java.io.Serializable?

Generally not. Joshua Bloch says to implement Serializable judiciously. A summary of drawbacks that he describes:
decreases flexibility of changing class implementation later - the serialized form is part of the class's API
makes some bugs and security holes more likely - an attacker can access class internals within the serialized byte stream
increases test burden - now you have to test serialization!
burdens authors of subclasses - they have to make their subclasses Serializable too
Of course, sometimes you need a POJO to implement Serializable, say for RMI, but if the need isn't there, your code will be simpler and more secure without it.

Only if you need to be able to serialise them. It's not worth the effort otherwise.

It depends more on the needs. In the context of web applications, some web servers (eg. Tomcat 6) even make it mandatory to serialize the classes whose objects we store in sessions.

One thing I've done to address the fact that the serialized form is not backwards compatible (say when dynamically reloading a class on a running system), is load the fields I want to save into a hashmap and then serializing that. That way, I can always deserialize in the data, even if there are missing fields. You might have to provide defaults for missing keys, but it's better than messing up field order.